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Expert Institute Interview Questions

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Data Structures & Algorithms

Given two sorted lists, write a function to merge them into one sorted list.

Merge Sorted Lists

Given a list of integers, and an integer N, write a function to find all combinations that sum to the value N.

Sum to N

Given two nonempty lists of user_ids and tips, write a function to find the user that tipped the most.

Biggest Tip

Given a list of tuples featuring names and grades on a test, write a function to normalize the values of the grades to a linear scale between 0 and 1.

Normalize Grades

Stop Words Filter

Machine Learning

Encoding Categorical Features

How do we give each rejected applicant a reason why they got rejected?

Rejection Reason

Job Recommendation

Bank Fraud Model

Lasso vs Ridge

Probability

First to Six

500 Cards

Raining in Seattle

Found Item

Given three uniform(0,4) random variables, what is the probability that the median of them is greater than 3?

Median Probability

A/B Testing

Experiment Validity

Delivery Estimate Model

Button AB Test

A/B Test Power Size

Green Dot

Write a query to select the top 3 departments with at least ten employees and rank them according to the percentage of their employees making over 100K in salary.

Employee Salaries

Select the 2nd highest salary in the engineering department

2nd Highest Salary

User Experience Percentage

Distance Traveled

Write a query to retrieve the number of users that have posted each job only once and the number of users that have posted at least one job multiple times.

Repeat Job Postings

<p>Let’s say that your company is running a standard control and variant AB test on a feature to increase conversion rates on the landing page. The PM checks the results and finds a .04 p-value.</p>

<p>How would you assess the validity of the result?</p>


<p>Write a SQL query to select the 2nd highest salary in the engineering department.</p>

<p><strong>Note:</strong> If more than one person shares the highest salary, the query should select the next highest salary.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>employees</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>first_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>last_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>department_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>departments</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


<p>Given a table called <code>user_experiences</code>, write a query to determine the percentage of users that held the title of <code>&#34;Data Analyst&#34;</code> immediately before holding the title <code>&#34;Data Scientist&#34;</code>.</p>

<p>Immediate is defined as the user holding no other titles between the <code>&#34;Data Analyst&#34;</code> and <code>&#34;Data Scientist&#34;</code> roles.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>user_experiences</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>position_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>start_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>end_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>percentage</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>


<p>Given a <code>employees</code> and <code>departments</code> table, select the top 3 departments with at least ten employees and rank them according to the percentage of their employees making over 100K in salary.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>employees</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>first_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>last_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>department_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>departments</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>percentage_over_100k</code></td>
<td>FLOAT</td>
</tr>

<tr>
<td><code>department_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>number_of_employees</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


<p>Imagine a deck of 500 cards numbered from 1 to 500. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what’s the probability of each subsequent card being larger than the previous drawn card?</p>


<p>Imagine a deck of 2000 cards numbered from 1 to 2000. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what’s the probability of each subsequent card being larger than the previously drawn card?</p>


Imagine a deck of 2000 cards numbered from 1 to 2000. If all the cards are shuffled randomly and you are asked to pick three cards, one at a time, what's the probability of each subsequent card being larger than the previously drawn card?

2000 cards

<p>Let’s say you want to test the close friends feature on Instagram Stories.</p>

<p>How would you make a control group and test group to account for network effects?</p>


<p>What could be a potential risk when Facebook segments the metrics of the user interface change by market or demographic groups?</p>

What could be a potential risk when Facebook segments the metrics of the user interface change by market or demographic groups?

Network Experiment Design I

<p>What is the primary metric that Facebook should monitor if it decides to make the user interface of its posting feature more like Instagram's?</p>

What is the primary metric that Facebook should monitor if it decides to make the user interface of its posting feature more like Instagram's?

Network Experiment Design II

<p>If Facebook changes its user interface to mimic Instagram's, which adverse effect should they anticipate and monitor?</p>

If Facebook changes its user interface to mimic Instagram's, which adverse effect should they anticipate and monitor?

Network Experiment Design III

Network Experiment Design

<p>Given two sorted lists, write a function to merge them into one sorted list.</p>

<p><em>Bonus: What’s the time complexity?</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">list1</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span>
</span></span><span class="line"><span class="cl"><span class="n">list2</span> <span class="o">=</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">6</span><span class="p">]</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="k">def</span> <span class="nf">merge_list</span><span class="p">(</span><span class="n">list1</span><span class="p">,</span><span class="n">list2</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">]</span>
</span></span></code></pre>


<p>You have two sorted lists, one with m elements and one with n elements. What would be the time complexity of merging the two lists via merge sort?</p>


You have two sorted lists, one with m elements and one with n elements. What would be the time complexity of merging the two lists via merge sort? 

Merging Lists Complexity

<p>Amy and Brad take turns in rolling a fair six-sided die. Whoever rolls a “6” first wins the game. Amy starts by rolling first.</p>

<p>What’s the probability that Amy wins?</p>


Amy and Brad take turns in rolling a fair six-sided die. Whoever rolls a “6” first wins the game. Amy starts by rolling first.

What’s the probability that Amy wins?

<p>Given the tables <code>users</code> and <code>rides</code>, write a query to report the distance traveled by each user in descending order.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>users</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>rides</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>passenger_user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>distance</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>distance_traveled</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>


<p>Let’s say at Netflix we offer a subscription where customers can enroll for a 30-day free trial. After 30 days, customers will be automatically charged based on the package selected.</p>

<p>Let’s say we want to measure the success of acquiring new users through the free trial.</p>

<p>How can we measure acquisition success and what metrics can we use to measure the success of the free trial?</p>


<p>Let’s say we want to measure the effectiveness of Netflix’s 30-day free trial plan.</p>

<p>What is NOT a metric we would use?</p>


Let's say we want to measure the effectiveness of Netflix's 30-day free trial plan.

What is NOT a metric we would use?

Netflix Retention

How do we measure the success of acquiring new users through a free trial

Product Sense & Metrics

<p>Let’s say that you’re a data scientist on the engagement team. A product manager comes up to you and says that the weekly active users metric is up 5% but email notification open rates are down 2%.</p>

<p>What would you investigate to diagnose what’s happening?</p>


Email Open Rate

WAU vs Open Rates

<p>Given two tables:  <code>accounts</code>, and <code>downloads</code>, find the average number of downloads for free vs paying accounts, broken down by day.</p>

<p><em>Note: You only need to consider accounts that have had at least one download before when calculating the average.</em></p>

<p><em>Note: round <code>average_downloads</code> to 2 decimal places.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>accounts</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>account_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>paying_customer</code></td>
<td>BOOLEAN</td>
</tr>
</tbody>
</table>
<p><code>downloads</code> table</p>

<table>
<thead>
<tr>
<th>column</th>
<th>type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>account_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>download_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>downloads</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>download_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>paying_customer</code></td>
<td>BOOLEAN</td>
</tr>

<tr>
<td><code>average_downloads</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>


Download Facts

<p>Given a dictionary with weights, write a function <code>random_key</code> that returns a key at random with a probability proportional to the weights.</p>

<p><strong>Example 1:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">weights</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;A&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s1">&#39;B&#39;</span><span class="p">:</span> <span class="mi">2</span><span class="p">}</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">random_key</span><span class="p">(</span><span class="n">weights</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="k">return</span> <span class="n">A</span> <span class="mi">1</span><span class="o">/</span><span class="mi">3</span> <span class="n">of</span> <span class="n">the</span> <span class="n">time</span><span class="p">,</span> <span class="n">B</span> <span class="mi">2</span><span class="o">/</span><span class="mi">3</span> <span class="n">of</span> <span class="n">the</span> <span class="n">time</span>
</span></span></code></pre>

<p><strong>Example 2:</strong></p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">weights</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;A&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="s1">&#39;B&#39;</span><span class="p">:</span> <span class="mi">1</span><span class="p">}</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">random_key</span><span class="p">(</span><span class="n">weights</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="k">return</span> <span class="n">A</span> <span class="mi">1</span><span class="o">/</span><span class="mi">2</span>  <span class="n">of</span> <span class="n">the</span> <span class="n">time</span><span class="p">,</span> <span class="n">B</span> <span class="mi">1</span><span class="o">/</span><span class="mi">2</span>  <span class="n">of</span> <span class="n">the</span> <span class="n">time</span>
</span></span></code></pre>


Weighted Keys

<p>Let’s say that you work at a B2B SAAS company that’s interested in testing the pricing of different levels of subscriptions.</p>

<p>Your project manager comes to you and asks you to run a two-week-long A/B test to test an increase in pricing.</p>

<p>How would you approach designing this test?  How would you determine whether the increase in pricing is a good business decision?</p>


Testing Price Increase

<p>A team wants to A/B test multiple different changes through a sign-up funnel.</p>

<p>For example, on a page, a button is currently red and at the top of the page. They want to see if changing a button from red to blue and/or from the top of the page to the bottom of the page will increase click-through.</p>

<p>How would you set up this test?</p>


<p>Your team wants to run an AB test on the color (red or blue) and position (top/bottom of the page) of a button that links to a promotion.</p>

<p>How many different variants of the test should you run to see the effect that a red button has on the bottom of the page, if currently the button is blue and on the top of the page.</p>


Your team wants to run an AB test on the color (red or blue) and position (top/bottom of the page) of a button that links to a promotion.

How many different variants of the test should you run to see the effect that a red button has on the bottom of the page, if currently the button is blue and on the top of the page.

A/B Test Variants

<p>You’re a data scientist working for a smart grocery platform that helps families automatically plan their Christmas dinner based on their dietary preferences and pantry availability.</p>

<p>Each Christmas recipe consists of several ingredients, and each ingredient has different brands with different prices. Families want the cheapest possible ingredient combination but only using brands they have marked as acceptable and only those ingredients they do not already have in their pantry.</p>

<p>Write a SQL query to determine the cheapest valid shopping cost for each recipe for family_id = 1, while also identifying whether the recipe is feasible to make.</p>

<p>For each recipe, compute:</p>

<ol>
<li><strong><code>missing_ingredients</code>:</strong> number of ingredients the family does not already have in their pantry</li>
<li><strong><code>min_total_cost</code>:</strong> total minimum cost required to buy missing ingredients</li>
<li>feasible:

<ul>
<li><code>&#39;Yes&#39;</code> if every missing ingredient has at least one acceptable brand available</li>
<li><code>&#39;No&#39;</code> otherwise (and <code>min_total_cost</code> should be <code>NULL</code>)</li>
</ul></li>
</ol>

<p><strong><em>Note:</em></strong> <em>Sort results by <code>missing_ingredients</code> ASC and <code>min_total_cost</code> ASC (NULLS LAST)</em></p>

<p><strong>Schema</strong></p>

<p><strong>Input</strong></p>

<p><strong><code>recipes</code> Table</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td>recipe_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>ingredient_id</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong><code>ingredient_brands</code> Table</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td>ingredient_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>brand_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>price</td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>
<p><strong><code>pantry</code> Table</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td>family_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>ingredient_id</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong><code>acceptable_brands</code> Table</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td>family_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>brand_id</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td>recipe_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>missing_ingredients</td>
<td>INTEGER</td>
</tr>

<tr>
<td>min_total_cost</td>
<td>DECIMAL</td>
</tr>

<tr>
<td>feasible</td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><strong>Example</strong></p>

<p><strong>Input</strong></p>

<p><strong><code>recipes</code> Table</strong></p>

<table>
<thead>
<tr>
<th>recipe_id</th>
<th>ingredient_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>100</td>
</tr>

<tr>
<td>1</td>
<td>200</td>
</tr>

<tr>
<td>1</td>
<td>300</td>
</tr>

<tr>
<td>2</td>
<td>200</td>
</tr>

<tr>
<td>2</td>
<td>400</td>
</tr>
</tbody>
</table>
<p><strong><code>pantry</code> Table</strong></p>

<table>
<thead>
<tr>
<th>family_id</th>
<th>ingredient_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>100</td>
</tr>
</tbody>
</table>
<p><strong><code>ingredient_brands</code> Table</strong></p>

<table>
<thead>
<tr>
<th>ingredient_id</th>
<th>brand_id</th>
<th>price</th>
</tr>
</thead>

<tbody>
<tr>
<td>200</td>
<td>10</td>
<td>3.50</td>
</tr>

<tr>
<td>200</td>
<td>11</td>
<td>2.99</td>
</tr>

<tr>
<td>300</td>
<td>20</td>
<td>8.50</td>
</tr>

<tr>
<td>400</td>
<td>30</td>
<td>6.75</td>
</tr>
</tbody>
</table>
<p><strong><code>acceptable_brands</code> Table</strong></p>

<table>
<thead>
<tr>
<th>family_id</th>
<th>brand_id</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>10</td>
</tr>

<tr>
<td>1</td>
<td>20</td>
</tr>

<tr>
<td>1</td>
<td>30</td>
</tr>
</tbody>
</table>
<p><strong>Output</strong></p>

<table>
<thead>
<tr>
<th>recipe_id</th>
<th>missing_ingredients</th>
<th>min_total_cost</th>
<th>feasible</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2</td>
<td>12.00</td>
<td>Yes</td>
</tr>

<tr>
<td>2</td>
<td>2</td>
<td>10.25</td>
<td>Yes</td>
</tr>
</tbody>
</table>

<h3><strong>Explanation</strong></h3>

<p>For Recipe 1, the required ingredients are 100, 200, and 300. The pantry already contains ingredient 100, so only 200 and 300 are missing. The cheapest acceptable option for ingredient 200 is brand 10 at $3.50, since brand 11 is not allowed. For ingredient 300, the cheapest acceptable option is brand 20 at $8.50. This makes the total cost $12.00, and the recipe is feasible.</p>

<p>For Recipe 2, the required ingredients are 200 and 400. The cheapest acceptable choice for ingredient 200 is again $3.50, and for ingredient 400 it is $6.75. The total comes to $10.25, and this recipe is also feasible.</p>


Write a SQL query to determine the cheapest valid shopping cost for each recipe for family_id = 1, while also identifying whether the recipe is feasible to make.

Christmas Dinner Ingredient Optimization

<p>Let’s say we want to build a new delivery time estimate model for consumers ordering food delivery.</p>

<p>How would you determine if the new model predicts delivery times better than the old model?</p>


<p>When rolling out a new delivery time estimate model in production, what is an important consideration?</p>

When rolling out a new delivery time estimate model in production, what is an important consideration?

Delivery Estimate Model I

<p>What is one way to measure the performance of a new delivery time estimate model for food delivery?</p>

What is one way to measure the performance of a new delivery time estimate model for food delivery?

Delivery Estimate Model II

<p>Given a table of job postings, write a query to retrieve the number of users that have posted each job only once and the number of users that have posted at least one job multiple times.</p>

<p>Each user has at least one job posting. Thus the sum of <code>single_post</code> and <code>multiple_posts</code> should equal the total number of distinct <code>user_id</code>’s.</p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>job_postings</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>job_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>date_posted</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>single_post</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>multiple_posts</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


<p>How would you measure the success of Facebook Groups?</p>


<p>Considering the purpose of Facebook Groups as a platform for connecting users through shared interests or real-life relationships, which metrics would be appropriate to measure the success of these groups?</p>


Considering the purpose of Facebook Groups as a platform for connecting users through shared interests or real-life relationships, which metrics would be appropriate to measure the success of these groups?

Group Success

<p>Write a Python function called <strong><code>max_profit</code></strong> that takes a list of integers, where the i-th integer represents the price of a given stock on day i, and returns the maximum profit you can achieve by buying and selling the stock.</p>

<p>You may complete, at most, two complete buy/sell transactions to maximize profits on a stock.</p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">prices</span> <span class="o">=</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="k">def</span> <span class="nf">max_profit</span><span class="p">(</span><span class="n">prices</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="mi">6</span>
</span></span></code></pre>

<p>Explanation:</p>

<pre><code>Buy on day 4 (price = 0) and sell on day 6 (price = 3): profit = 3 - 0 = 3.
Then buy again on day 7 (price = 1) and sell on day 8 (price = 4): profit = 4 - 1 = 3.
Total profit: 3 + 3 = 6.
</code></pre>


Maximum Profit

<p>In an A/B test, how can you check if assignment to the various buckets was truly random?</p>


<p>In an A/B test, which of the following is a common method to determine if the assignment to the test groups was truly random?</p>

In an A/B test, which of the following is a common method to determine if the assignment to the test groups was truly random?

Random Bucketing

<p>You are about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each independently if it’s raining. Each of your friends has a <sup>2</sup>⁄<sub>3</sub> chance of telling you the truth and a <sup>1</sup>⁄<sub>3</sub> chance of messing with you by lying. All 3 friends tell you that “Yes” it is raining.</p>

<p>What is the probability that it’s actually raining in Seattle?</p>


<p>What is the <strong>main</strong> difference between the Frequentist and Bayesian methods of probabilistic analysis?</p>


What is the **main** difference between the Frequentist and Bayesian methods of probabilistic analysis?

Frequentist Vs Bayesian Analysis

<p>Over budget on a project is defined when the salaries, prorated to the day, exceed the budget of the project.</p>

<p>For example, if Alice and Bob both combined income make 200K and work on a project of a budget of 50K that takes half a year, then the project is over budget given 0.5 * 200K = 100K &gt; 50K.</p>

<p>Write a query to forecast the budget for all projects and return a label of <code>&#34;overbudget&#34;</code> if it is over budget and <code>&#34;within budget&#34;</code> otherwise.</p>

<p><em>Note: Assume that employees only work on one project at a time.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>employees</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>first_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>last_name</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>salary</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>department_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><code>projects</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>title</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>state_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>end_date</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>budget</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>departments</strong> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>name</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>
<p><code>employee_projects</code> table</p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>project_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>employee_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Column</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>title</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>project_forecast</code></td>
<td>VARCHAR</td>
</tr>
</tbody>
</table>


Over-Budget Projects

<p>Netflix has hired people to rate movies.</p>

<p>Out of all of the raters, 80% of the raters carefully rate movies and rate 60% of the movies as good and 40% as bad. The other 20% are lazy raters and rate 100% of the movies as good.</p>

<p>Assuming all raters rate the same amount of movies, what is the probability that a movie is rated good?</p>


<p>There are two categories of movie raters: careful and lazy. Careful raters make up 80% of the total. They rate 60% of the movies as good and 40% as bad. Lazy raters, constitute 20% of the raters and 100% of the movies as good. Given these parameters, calculate the overall probability of a movie being rated good.</p>

There are two categories of movie raters: careful and lazy. Careful raters make up 80% of the total. They rate 60% of the movies as good and 40% as bad. Lazy raters, constitute 20% of the raters and 100% of the movies as good. Given these parameters, calculate the overall probability of a movie being rated good.

Lazy Raters

<p>Let’s say you’re given all the different marketing channels along with their respective marketing costs at a company called Mode, that sells B2B analytics dashboards.</p>

<p>What metrics would you use to determine the value of each marketing channel?</p>


<p>When determining the value of each marketing channel for the company Mode, which metric is considered the key metric?</p>

When determining the value of each marketing channel for the company Mode, which metric is considered the key metric?

Marketing Channel Metrics

What metrics would you use to determine the value of each marketing channel?

Analytics

<p>What is an unbiased estimator and can you provide an example for a layman to understand?</p>


What makes an estimator of a population statistic unbiased?

Unbiased Estimator

Statistics

<p>Given the <code>transactions</code> table below, write a query that finds the third purchase of every user.</p>

<p><em>Note: Sort the results by the <code>user_id</code> in ascending order. If a user purchases two products at the same time, the lower <code>id</code> field is used to determine which is the first purchase.</em></p>

<p><strong>Example:</strong></p>

<p><strong>Input:</strong></p>

<p><code>transactions</code> table</p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>product_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>quantity</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
<p><strong>Output:</strong></p>

<table>
<thead>
<tr>
<th>Columns</th>
<th>Type</th>
</tr>
</thead>

<tbody>
<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>

<tr>
<td><code>product_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>quantity</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>


Third Purchase

<p>Given a list of <code>integers</code>, and an integer <code>N</code>, write a function <code>sum_to_n</code> to find all combinations that sum to the value <code>N</code>.</p>

<p><strong>Example:</strong> </p>

<p><strong>Input:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="n">integers</span> <span class="o">=</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span>
</span></span><span class="line"><span class="cl"><span class="n">N</span> <span class="o">=</span> <span class="mi">8</span>
</span></span></code></pre>

<p><strong>Output:</strong></p>

<pre tabindex="0" class="chroma"><code><span class="line"><span class="cl"><span class="k">def</span> <span class="nf">sum_to_n</span><span class="p">(</span><span class="n">integers</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span> <span class="o">-&gt;</span>
</span></span><span class="line"><span class="cl"> <span class="p">[</span>
</span></span><span class="line"><span class="cl">  <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">],</span>
</span></span><span class="line"><span class="cl">  <span class="p">[</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">],</span>
</span></span><span class="line"><span class="cl">  <span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span>
</span></span><span class="line"><span class="cl"><span class="p">]</span>
</span></span></code></pre>


<p>Let’s say you’re a Product Data Scientist at Instagram. How would you measure the success of the Instagram TV product?</p>


<p>What is the primary goal of Instagram TV as a product feature?</p>

What is the primary goal of Instagram TV as a product feature?

Instagram TV Success

<p>Let’s say you’re a data scientist at LinkedIn where you’re working on a product that sends qualified job candidates to companies. The team has launched a new feature that allows candidates to message hiring managers at companies directly during the interview process to get updates on their status.</p>

<p>Due to engineering constraints, the company can’t AB test the feature before launching it.</p>

<p>How would you analyze how the feature is performing?</p>


How would you analyze how the feature is performing?

Recruiting Leads

Challenge

<h3>Job Description</h3><div>Job Description<div>Company Description<br><br><p>Expert Institute is the #1 technology platform connecting litigation attorneys with expert witnesses. We operate in a multi-billion-dollar market with massive untapped potential (~2% market share today). With thousands of law firm clients nationwide and 1M+ experts on our platform, we're scaling quickly—and looking for elite engineering talent to help architect the next phase of growth.</p>Job Description<br><br><p>We're looking for a <strong>Staff Software Engineer </strong>to serve as a technical leader and architect for the products powering our two-sided marketplace. You'll set the technical direction for critical systems, drive architectural decisions that shape our platform for years to come, and mentor engineers across the organization. From designing AI-powered document processing pipelines to architecting the data infrastructure behind our case-matching intelligence, you'll operate at the intersection of deep technical craft and high-leverage business impact.</p><p>This role is for a seasoned engineer who has already done the "senior engineer" job well and is ready to expand their scope—influencing systems, teams, and the technical strategy of the company. You'll partner directly with engineering leadership, Product, and Design to translate ambitious business goals into resilient, scalable technical realities.</p><p>What You'll Do</p><ul><li><p><strong>Architect and lead</strong> the design of complex, distributed systems that power our marketplace at scale, including our AI/ML infrastructure, search and matching services, and data platform</p></li><li><p><strong>Drive technical strategy</strong> across multiple teams and services—setting standards for reliability, performance, security, and developer experience</p></li><li><p><strong>Own our AWS cloud infrastructure </strong>end-to-end: VPC design, compute (ECS/EKS/Lambda), data stores (RDS, DynamoDB, S3), networking, IAM, observability, and cost optimization</p></li><li><p><strong>Design and evolve our data platform</strong>—including data modeling, ETL/ELT pipelines, warehousing (e.g., <span class="long-word">Redshift/Snowflake),</span> streaming architectures, and the data foundations that power analytics and ML</p></li><li><p><strong>Lead the technical design </strong>of AI-powered features, including LLM-backed document processing, embeddings/vector search for expert matching, RAG pipelines, and evaluation frameworks</p></li><li><p><strong>Establish engineering excellence: </strong>define coding standards, CI/CD practices, testing strategies, incident response processes, and operational maturity across the org</p></li><li><p><strong>Mentor engineers </strong>at all levels—through code review, design review, pairing, and career coaching—raising the bar for the entire team</p></li><li><p><strong>Partner with leadership</strong> on technical roadmap, hiring, org design, and build-vs-buy decisions</p></li><li><p><strong>Own critical production systems</strong> including on-call rotation leadership, SLO definition, and driving postmortems that translate incidents into lasting improvements</p></li><li><p><strong>Identify and resolve </strong>systemic performance, scalability, and reliability bottlenecks before they become customer-facing problems</p></li></ul>Qualifications<br><br><p>We're looking for candidates who are:</p><ul><li><p>Seasoned technical leaders who thrive in ambiguity and can turn vague goals into concrete architectures</p></li><li><p>Deeply curious about AI/ML and actively shipping production systems using modern techniques (LLMs, embeddings, vector DBs, agentic workflows)</p></li><li><p>Strong generalists with depth in distributed systems, cloud infrastructure, and data engineering</p></li><li><p>Expert-level in Node.js, TypeScript, and PostgreSQL, with working fluency across additional languages and datastores</p></li><li><p>Force multipliers who make the engineers around them better</p></li></ul><br><br>Additional Information<br><br><p>The right candidates have:</p><ul><li><p><strong>8+ years </strong>of professional engineering experience, with at least 2+ years operating at a Staff or equivalent level of scope and influence</p></li><li><p><strong>Deep AWS expertise</strong>—you've designed, built, and operated production workloads across compute, storage, networking, and managed services; you understand the trade-offs between ECS vs. EKS vs. Lambda, when to reach for Aurora vs. DynamoDB, and how to keep a cloud bill sane as you scale</p></li><li><p><strong>Infrastructure-as-code fluency </strong>with Terraform, CDK, or Pulumi, and a strong grasp of CI/CD, containerization (Docker), and modern deployment practices</p></li><li><p><strong>Data engineering chops:</strong> you've designed production data models, built reliable pipelines (Airflow, dbt, Kafka, or equivalent), and shipped warehouse-backed analytics or ML features</p></li><li><p><strong>Architectural range: </strong>you can zoom from individual service design up to multi-system architecture, and you have strong opinions—loosely held—about microservices vs. monoliths, event-driven design, API design, and data consistency models</p></li><li><p><strong>AI/ML production experience: </strong>you've shipped features backed by LLMs, embedding models, or traditional ML, and you understand the infrastructure, evaluation, and cost considerations that come with them</p></li><li><p><strong>Outstanding communication skills</strong>—you can write a crisp RFC, run a productive design review, explain a complex system to a non-technical stakeholder, and give feedback that actually changes behavior</p></li><li><p><strong>A track record of mentorship</strong> and elevating the engineers around you</p></li><li><p><strong>Strong product intuition</strong>—you push back on bad specs, you understand why we're building what we're building, and you use that context to make better technical decisions</p></li><li><p><strong>A bias to action </strong>balanced with the judgment to know when to slow down and design carefully</p></li><li><p><strong>Deep interest </strong>in our product, our customers, and the legal industry's transformation through technology</p></li></ul><p>All your information will be kept confidential according to EEO guidelines.</p></div></div>

<h3>Job Description</h3><div>Job Description<div>Company Description<br><br><p>We operate in a fast-paced environment where hiring needs evolve quickly. This position is not currently open, but we encourage talented candidates interested in this role to connect with us</p><p>This is an <strong>entry-level, full-time, hybrid</strong> position based in our Milwaukee office</p><p><br />We cannot provide Work Visa support for this role at this time.<br><br> ABOUT US</p><p>Expert Institute is the nation's leading expert consulting and insights platform, helping client law firms win more cases and increase their client outcomes. Established in 2010, Expert Institute has grown significantly to support over 5,000 of the best law firms nationwide, across all areas of practice.</p><p>We connect litigators with top industry experts, innovative litigation research, physician consultations, and comprehensive due diligence — all delivered through our SaaS platform, Expert iQ, leveraging proprietary data and analytics, to give our client law firms a winning edge for everyone they represent<br><br> At Expert Institute, at our core, we provide exceptional tools and resources for trial attorneys. Trial attorneys who want the best outcome for their clients. <strong>Trial work is demanding and intense and so is the work we do every day at Expert Institute.</strong> We believe a winning spirit requires a relentless commitment to high performance and that we win as a team. And everyone on the team will do their best every day to make sure we win together.<br /> That's a winning mindset. If you have it, we'd love to hear from you.</p>Job Description<br><br><p>Are you passionate about research, communication, and the legal industry? Do you thrive in a fast-paced, client-focused environment? Join our team as a <strong>Research Analyst</strong>, where you'll play a critical role in identifying, evaluating, and connecting expert witnesses with attorneys handling high-stakes litigation.</p><p>This is a unique but demanding opportunity for individuals looking to build a career in client consulting, legal research, or professional services. Research Analysts serve as the backbone of our <strong>Expert Search</strong> service, sourcing, screening, and vetting expert witness candidates to support our attorney clients. You’ll engage with subject matter experts across industries, assessing their suitability for complex legal matters and providing data-driven recommendations that directly impact case outcomes.</p><p><strong>What You’ll Do:</strong></p><ul><li>Manage multiple cases with varying deadlines, conducting in-depth research to understand each matter’s unique needs.</li><li>Identify and engage with both existing contacts and new candidates to expand our network of expert professionals.</li><li>Conduct outreach via phone and email to screen potential expert witnesses and assess their qualifications.</li><li>Deliver thoroughly researched and well-vetted expert recommendations tailored to clients’ litigation strategies.</li><li>Build and maintain relationships with experts, providing insight into our process and ensuring timely follow-up.</li><li>Collaborate closely with internal teams to ensure seamless service delivery and an exceptional client experience.</li></ul>Qualifications<br><br><p> </p><ul><li>A desire for a promising career (not just a job) and a willingness to put in the time to succeed.</li><li>A corporate internship or relevant experience is beneficial.</li><li><strong>Strong communication skills</strong>, both written and verbal, with the ability to engage professionally on the phone with experts and attorneys.</li><li><strong>A client-focused mindset</strong> – prior customer service, research, or consulting experience is a huge plus.</li><li><strong>Critical thinking and attention to detail</strong> to assess expert credentials and case requirements effectively.</li><li><strong>A self-motivated, competitive drive</strong>, with the ability to multitask and work autonomously.</li><li><strong>A collaborative, team-oriented approach</strong> with a commitment to excellence.</li><li><strong>Tech-savvy and adaptable</strong>, comfortable using cloud-based solutions like Salesforce.</li><li><strong>A bachelor’s degree, in a major with research as a foundation, is beneficial but not required</strong></li></ul><br><br>Additional Information<br><br><p><strong>Why Join Us?</strong></p><ul><li>Gain <strong>insider exposure to the legal industry</strong> and high-profile litigation.</li><li>Develop <strong>invaluable research and analytical skills</strong> applicable across industries.</li><li>Work in a dynamic, fast-paced environment where no two cases are the same.</li><li>Be part of a <strong>team that values curiosity, innovation, and professional growth</strong>.</li><li>And, in addition to best in class benefits, including a 401(k) match, we provide lunch in the office on Wednesday and Friday.</li></ul><p>This role operates<strong> Monday - Friday 8:00AM - 5:00 PM CST (Hybrid)</strong></p><p><br /> If you’re looking for an engaging role that blends research, communication, and client service, we’d love to hear from you!</p><p>All your information will be kept confidential according to EEO guidelines.</p></div></div>

Calculate Moving Average	SQL	Easy
Predict Customer Churn	Machine Learning	Medium
A/B Test Significance	Statistics	Medium
Optimize Query Performance	SQL	Hard
Feature Importance Analysis	Machine Learning	Medium
Clean Missing Data	Python	Easy
Neural Network Architecture	Deep Learning	Hard
Calculate Cohort Retention	SQL	Medium
Bayesian Probability	Statistics	Easy
Recommend Similar Products	Machine Learning	Hard

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