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Nuance Communications Interview Questions

Nuance Communications Interview Guides

Data Structures & Algorithms

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

Merge Sorted Lists

Find Bigrams

Write a function to create a single dataframe with complete addresses in the format of street, city, state, zip code.

Complete Addresses

Write a function friendship_timeline to generate an output that lists the pairs of friends with their corresponding timestamps of the friendship beginning and then the timestamp of the friendship ending. 

Friendship Timeline

String Shift

Probability

First to Six

500 Cards

Raining in Seattle

Found Item

Ad Raters

Machine Learning

Coefficients of Logistic Regression

Job Recommendation

RMS Error

Why would one algorithm generate different success rates with the same dataset?

Same Algorithm Different Success

Lasso vs Ridge

A/B Testing

Experiment Validity

Delivery Estimate Model

Button AB Test

A/B Test Power Size

Network Experiment Design

Statistics

Write a function to return the cumulative percentage of students that received scores within certain buckets.

Bucket Test Scores

P-value to a Layman

Reducing Error Margin

What are the assumptions of linear regression?

Assumptions of Linear Regression

Possibly Biased Coin

We’re given two tables, a <code>users</code> table with demographic information and the neighborhood they live in and a <code>neighborhoods</code> table.

Write a query that returns all neighborhoods that have 0 users. 

Example:

Input:

<code>users</code> table

<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>

<tr>
<td><code>neighborhood_id</code></td>
<td>INTEGER</td>
</tr>

<tr>
<td><code>created_at</code></td>
<td>DATETIME</td>
</tr>
</tbody>
</table>
<code>neighborhoods</code> table

<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>

<tr>
<td><code>city_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
Output:

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

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

Write a query that returns all neighborhoods that have 0 users.

Empty Neighborhoods

Write a SQL query to select the 2nd highest salary in the engineering department.

Note: If more than one person shares the highest salary, the query should select the next highest salary.

Example:

Input:

<code>employees</code> table

<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>
<code>departments</code> table

<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>
Output:

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

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

Select the 2nd highest salary in the engineering department

2nd Highest Salary

Given the <code>employees</code> and <code>departments</code> table, write a query to get the top 3 highest employee salaries by department. If the department contains less that 3 employees, the top 2 or the top 1 highest salaries should be listed (assume that each department has at least 1 employee). 

Note: The output should include the full name of the employee in one column, the department name, and the salary. The output should be sorted by department name in ascending order and salary in descending order. 

Example:

Input:

<code>employees</code> table

<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>
<code>departments</code> table

<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>
Output:

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

<tbody>
<tr>
<td><code>employee_nam</code>e</td>
<td>VARCHAR</td>
</tr>

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

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

Get the top 3 highest employee salaries by department

Top Three Salaries

The schema below is for a retail online shopping company consisting of two tables, <code>attribution</code> and <code>user_sessions</code>.

<ul>
<li>The attribution table logs a session visit for each row.</li>

<li>If <code>conversion</code> is <code>true</code>, then the user converted to buying on that session.</li>

<li>The <code>channel</code> column represents which advertising platform the user was attributed to for that specific session.</li>

<li>Lastly the <code>user_sessions</code> table maps many to one session visits back to one user.</li>
</ul>

First touch attribution is defined as the channel with which the converted user was associated when they first discovered the website.

Calculate the first touch attribution for each <code>user_id</code> that converted. 

Example:

Input:

<code>attribution</code> table

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

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

<tr>
<td><code>channel</code></td>
<td>VARCHAR</td>
</tr>

<tr>
<td><code>conversion</code></td>
<td>BOOLEAN</td>
</tr>
</tbody>
</table>
<code>user_sessions</code> table

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

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

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

<tr>
<td><code>user_id</code></td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
Example output:

<table>
<thead>
<tr>
<th><code>user_id</code></th>
<th><code>channel</code></th>
</tr>
</thead>

<tbody>
<tr>
<td>123</td>
<td>facebook</td>
</tr>

<tr>
<td>145</td>
<td>google</td>
</tr>

<tr>
<td>153</td>
<td>facebook</td>
</tr>

<tr>
<td>172</td>
<td>organic</td>
</tr>

<tr>
<td>173</td>
<td>email</td>
</tr>
</tbody>
</table>

Calculate the first touch attribution for each `user_id` that converted.

First Touch Attribution

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

Bonus: What’s the time complexity?

Example:

Input:

<pre tabindex="0" class="chroma"><code>list1 = [1,2,5]
list2 = [2,4,6]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def merge_list(list1,list2) -&gt; [1,2,2,4,5,6]
</code></pre>

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?

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

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?

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?

Given a table of bank transactions with columns <code>id</code>, <code>transaction_value</code>, and <code>created_at</code> representing the date and time for each transaction, write a query to get the last transaction for each day.

The output should include the id of the transaction, datetime of the transaction, and the transaction amount. Order the transactions by datetime.

Example:

Input:

<code>bank_transactions</code> table

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

<tr>
<td><code>transaction_value</code></td>
<td>FLOAT</td>
</tr>
</tbody>
</table>
Output:

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

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

<tr>
<td><code>transaction_value</code></td>
<td>FLOAT</td>
</tr>

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

Last Transaction

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.

How would you assess the validity of the result?

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?

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?

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

Given two strings <code>A</code> and <code>B</code>, write a function <code>can_shift</code> to return whether or not <code>A</code> can be shifted some number of places to get <code>B</code>.

Example:

Input:

<pre tabindex="0" class="chroma"><code>A = &#39;abcde&#39;
B = &#39;cdeab&#39;
can_shift(A, B) == True

A = &#39;abc&#39;
B = &#39;acb&#39;
can_shift(A, B) == False
</code></pre>

Write a function <code>minimum_change</code> to find the minimum number of coins that make up the given amount of change <code>cents</code>. Assume we only have coins of value 1, 5, 10, and 25 cents.

Example:

Input:

<pre tabindex="0" class="chroma"><code>cents = 73
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def minimum_change(cents) -&gt; 7
#(25 + 25 + 10 + 10 + 1 + 1 + 1)
</code></pre>

Minimum Change

Netflix has hired people to rate movies.

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.

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

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.

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

A jar holds 1000 coins. Out of all of the coins, 999 are fair and one is double-sided with two heads. Picking a coin at random, you toss the coin ten times.

Given that you see 10 heads, what is the probability that the coin is double headed and the probability that the next toss of the coin is also a head?

Jars and Coins

Let’s say you’re given a dataframe of standardized test scores from high schoolers from grades 9 to 12 called df_grades.

Given the dataset, write code function in Pandas called bucket_test_scores to return the cumulative percentage of students that received scores within the buckets of &lt;50, &lt;75, &lt;90, &lt;100.

Example:

Input:

<pre tabindex="0" class="chroma"><code>print(df_grades)
</code></pre>

<table>
<thead>
<tr>
<th>user_id</th>
<th>grade</th>
<th>test score</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>10</td>
<td>85</td>
</tr>

<tr>
<td>2</td>
<td>10</td>
<td>60</td>
</tr>

<tr>
<td>3</td>
<td>11</td>
<td>90</td>
</tr>

<tr>
<td>4</td>
<td>10</td>
<td>30</td>
</tr>

<tr>
<td>5</td>
<td>11</td>
<td>99</td>
</tr>
</tbody>
</table>
Output:

<pre tabindex="0" class="chroma"><code>def bucket_test_scores(df_grades) -&gt;
</code></pre>

<table>
<thead>
<tr>
<th>grade</th>
<th>test score</th>
<th>percentage</th>
</tr>
</thead>

<tbody>
<tr>
<td>10</td>
<td>&lt;50</td>
<td>33%</td>
</tr>

<tr>
<td>10</td>
<td>&lt;75</td>
<td>66%</td>
</tr>

<tr>
<td>10</td>
<td>&lt;90</td>
<td>100%</td>
</tr>

<tr>
<td>10</td>
<td>&lt;100</td>
<td>100%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;50</td>
<td>0%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;75</td>
<td>0%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;90</td>
<td>50%</td>
</tr>

<tr>
<td>11</td>
<td>&lt;100</td>
<td>100%</td>
</tr>
</tbody>
</table>

You’re given two dataframes. One contains information about addresses and the other contains relationships between various cities and states:

Example:

<code>df_addresses</code>

<table>
<thead>
<tr>
<th>address</th>
</tr>
</thead>

<tbody>
<tr>
<td>4860 Sunset Boulevard, San Francisco, 94105</td>
</tr>

<tr>
<td>3055 Paradise Lane, Salt Lake City, 84103</td>
</tr>

<tr>
<td>682 Main Street, Detroit, 48204</td>
</tr>

<tr>
<td>9001 Cascade Road, Kansas City, 64102</td>
</tr>

<tr>
<td>5853 Leon Street, Tampa, 33605</td>
</tr>
</tbody>
</table>
<code>df_cities</code>

<table>
<thead>
<tr>
<th>city</th>
<th>state</th>
</tr>
</thead>

<tbody>
<tr>
<td>Salt Lake City</td>
<td>Utah</td>
</tr>

<tr>
<td>Kansas City</td>
<td>Missouri</td>
</tr>

<tr>
<td>Detroit</td>
<td>Michigan</td>
</tr>

<tr>
<td>Tampa</td>
<td>Florida</td>
</tr>

<tr>
<td>San Francisco</td>
<td>California</td>
</tr>
</tbody>
</table>
Write a function <code>complete_address</code> to create a single dataframe with complete addresses in the format of street, city, state, zip code.

Input:

<pre tabindex="0" class="chroma"><code>import pandas as pd

addresses = {&#34;address&#34;: [&#34;4860 Sunset Boulevard, San Francisco, 94105&#34;, &#34;3055 Paradise Lane, Salt Lake City, 84103&#34;, &#34;682 Main Street, Detroit, 48204&#34;, &#34;9001 Cascade Road, Kansas City, 64102&#34;, &#34;5853 Leon Street, Tampa, 33605&#34;]}

cities = {&#34;city&#34;: [&#34;Salt Lake City&#34;, &#34;Kansas City&#34;, &#34;Detroit&#34;, &#34;Tampa&#34;, &#34;San Francisco&#34;], &#34;state&#34;: [&#34;Utah&#34;, &#34;Missouri&#34;, &#34;Michigan&#34;, &#34;Florida&#34;, &#34;California&#34;]}

df_addresses = pd.DataFrame(addresses)
df_cities = pd.DataFrame(cities)
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def complete_address(df_addresses,df_cities) -&gt;
</code></pre>

<table>
<thead>
<tr>
<th>address</th>
</tr>
</thead>

<tbody>
<tr>
<td>4860 Sunset Boulevard, San Francisco, California, 94105</td>
</tr>

<tr>
<td>3055 Paradise Lane, Salt Lake City, Utah, 84103</td>
</tr>

<tr>
<td>682 Main Street, Detroit, Michigan, 48204</td>
</tr>

<tr>
<td>9001 Cascade Road, Kansas City, Missouri, 64102</td>
</tr>

<tr>
<td>5853 Leon Street, Tampa, Florida, 33605</td>
</tr>
</tbody>
</table>

Write a function called <code>find_bigrams</code> that takes a sentence or paragraph of strings and returns a list of all its bigrams in order.

Note: A bigram is a pair of consecutive words.

Example:

Input:

<pre tabindex="0" class="chroma"><code>sentence = &#34;&#34;&#34;
Have free hours and love children? 
Drive kids to school, soccer practice 
and other activities.
&#34;&#34;&#34;
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def find_bigrams(sentence) -&gt;

 [(&#39;have&#39;, &#39;free&#39;),
 (&#39;free&#39;, &#39;hours&#39;),
 (&#39;hours&#39;, &#39;and&#39;),
 (&#39;and&#39;, &#39;love&#39;),
 (&#39;love&#39;, &#39;children?&#39;),
 (&#39;children?&#39;, &#39;drive&#39;),
 (&#39;drive&#39;, &#39;kids&#39;),
 (&#39;kids&#39;, &#39;to&#39;),
 (&#39;to&#39;, &#39;school,&#39;),
 (&#39;school,&#39;, &#39;soccer&#39;),
 (&#39;soccer&#39;, &#39;practice&#39;),
 (&#39;practice&#39;, &#39;and&#39;),
 (&#39;and&#39;, &#39;other&#39;),
 (&#39;other&#39;, &#39;activities.&#39;)]
</code></pre>

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

How would you make a control group and test group to account for network effects?

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

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

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?

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

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

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

Network Experiment Design III

Let’s say we have a very naive advertising platform. There is an audience of size A and a limited amount of impressions B.

Each of the impressions goes to just one user, defined at random. Every user in the audience has the same random chance of receiving each impression. 

<ol>
<li>Compute the probability that a user has exactly 0 impressions. </li>

<li>What’s the probability that every person has at least 1 impression?</li>
</ol>

Impression Reach

You’re given a string that may contain the characters <code>{</code>, <code>}</code>, <code>[</code>, <code>]</code>, <code>(</code>, and <code>)</code>.

Task: Verify that the string is balanced. A balanced string is one where every opening character, <code>{</code>, <code>[</code>, or <code>(</code>, has a corresponding closing character, <code>}</code>, <code>]</code>, or <code>)</code>.

Write a function called <code>is_balanced(string: str) -&gt; bool</code> which verifies the balance of a string.

Example:

<pre tabindex="0" class="chroma"><code>is_balanced(&#39;(())[]{}&#39;) -&gt; True
</code></pre>

<pre tabindex="0" class="chroma"><code>is_balanced(&#39;{([(){}])()}&#39;) -&gt; True
</code></pre>

<pre tabindex="0" class="chroma"><code>is_balanced(&#39;{}[]())&#39;) -&gt; False
</code></pre>

<hr/>

Write a function that tests whether a string of brackets is balanced.

The Brackets Problem

A digital health startup is analyzing ECG sensor data captured from wearable heart monitors. Each row in the dataset represents one heartbeat, including its timestamp and calculated heart rate at that moment.

The clinical team wants to detect tachycardia runs, periods where a patient’s heart rate stays above 100 bpm continuously for at least 10 seconds .

Write a SQL query to identify every valid tachycardia run and return:

<ol>
<li><code>patient_id</code></li>
<li><code>run_start</code>: timestamp of the first beat in the run</li>
<li><code>run_end</code>: timestamp of the last beat in the run</li>
<li><code>duration_seconds</code>: difference in seconds between start and end (rounded to 2 decimals)</li>
</ol>

Sort results by <code>patient_id</code>, then <code>run_start</code>.

Definition of a Tachycardia Run

<ul>
<li>All consecutive heartbeats must have <code>heart_rate &gt; 100</code></li>
<li>Total duration ≥ 10 seconds</li>
<li>Any gap ≥ 3 seconds between consecutive beats breaks the run</li>
</ul>

Note: A patient may have multiple separate runs.

Schema

Input

<code>ecg_readings</code> table

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

<tbody>
<tr>
<td>patient_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>timestamp</td>
<td>DATETIME</td>
</tr>

<tr>
<td>heart_rate</td>
<td>INTEGER</td>
</tr>
</tbody>
</table>
Output

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

<tbody>
<tr>
<td>patient_id</td>
<td>INTEGER</td>
</tr>

<tr>
<td>run_start</td>
<td>DATETIME</td>
</tr>

<tr>
<td>run_end</td>
<td>DATETIME</td>
</tr>

<tr>
<td>duration_seconds</td>
<td>DECIMAL</td>
</tr>
</tbody>
</table>
Example

Input

<code>ecg_readings</code> table

<table>
<thead>
<tr>
<th>patient_id</th>
<th>timestamp</th>
<th>heart_rate</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2025-03-01 10:00:00</td>
<td>98</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:02</td>
<td>105</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:04</td>
<td>110</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:07</td>
<td>108</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:12</td>
<td>107</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:15</td>
<td>85</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:20</td>
<td>120</td>
</tr>

<tr>
<td>1</td>
<td>2025-03-01 10:00:28</td>
<td>122</td>
</tr>
</tbody>
</table>
Output

<table>
<thead>
<tr>
<th>patient_id</th>
<th>run_start</th>
<th>run_end</th>
<th>duration_seconds</th>
</tr>
</thead>

<tbody>
<tr>
<td>1</td>
<td>2025-03-01 10:00:02</td>
<td>2025-03-01 10:00:12</td>
<td>10.00</td>
</tr>
</tbody>
</table>

<h3>Explanation</h3>

The high-rate streak from 10:00:02 to 10:00:12 forms one continuous sequence because each gap between timestamps (2 to 4, 4 to 7, and 7 to 12) is less than three seconds. This creates a valid 10-second run. The later high values at seconds 20 and 28 are separated by an eight-second gap, so they form a different sequence that is shorter than 10 seconds and is therefore ignored.

Write a SQL query to identify every valid tachycardia run.

Detecting ECG Tachycardia Runs

Let’s say we have a sample size of $n$. The margin of error for our sample size is 3.

How many more samples would we need to decrease the margin of error to 0.3?

Let's say we have a sample size of N. The margin of error for our sample size is 3.

How many more samples would we need to decrease the margin of error to 0.3?

Let's say we have a sample size of N. The margin of error for our sample size is 3.

How many more samples would we need to decrease the margin of error to 0.3?

We have a table called <code>song_plays</code> that tracks each time a user plays a song.

Write a query to return the number of songs played on each date for each user

NOTE: If a user played the same song twice during the day count should be two.

<code>song_plays</code> table

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

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

<tr>
<td><code>date_played</code></td>
<td><code>DATETIME</code></td>
</tr>

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

<tr>
<td><code>song_id</code></td>
<td><code>INTEGER</code></td>
</tr>
</tbody>
</table>
Output:

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

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

<tr>
<td><code>played_date</code></td>
<td>DATE</td>
</tr>

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

Write a SQL query to create an aggregation of the song count by date for each user.

Lifetime Plays

There are two lists of dictionaries representing friendship beginnings and endings: <code>friends_added</code> and <code>friends_removed</code>. Each dictionary contains the <code>user_ids</code> and <code>created_at</code> time of the friendship beginning /ending.

Write a function <code>friendship_timeline</code> to generate an output that lists the pairs of friends with their corresponding timestamps of the friendship beginning and then the timestamp of the friendship ending.

Note: There can be multiple instances over time when two people became friends and unfriended; only output lists when a corresponding friendship was removed.

Example:

Input:

<pre tabindex="0" class="chroma"><code>friends_added = [
 {&#39;user_ids&#39;: [1, 2], &#39;created_at&#39;: &#39;2020-01-01&#39;},
 {&#39;user_ids&#39;: [3, 2], &#39;created_at&#39;: &#39;2020-01-02&#39;},
 {&#39;user_ids&#39;: [2, 1], &#39;created_at&#39;: &#39;2020-02-02&#39;},
 {&#39;user_ids&#39;: [4, 1], &#39;created_at&#39;: &#39;2020-02-02&#39;}]

friends_removed = [
 {&#39;user_ids&#39;: [2, 1], &#39;created_at&#39;: &#39;2020-01-03&#39;},
 {&#39;user_ids&#39;: [2, 3], &#39;created_at&#39;: &#39;2020-01-05&#39;},
 {&#39;user_ids&#39;: [1, 2], &#39;created_at&#39;: &#39;2020-02-05&#39;}]
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>friendships = [{
 &#39;user_ids&#39;: [1, 2],
 &#39;start_date&#39;: &#39;2020-01-01&#39;,
 &#39;end_date&#39;: &#39;2020-01-03&#39;
 },
 {
 &#39;user_ids&#39;: [1, 2],
 &#39;start_date&#39;: &#39;2020-02-02&#39;,
 &#39;end_date&#39;: &#39;2020-02-05&#39;
 },
 {
 &#39;user_ids&#39;: [2, 3],
 &#39;start_date&#39;: &#39;2020-01-02&#39;,
 &#39;end_date&#39;: &#39;2020-01-05&#39;
 },
]
</code></pre>

You’re given a dataframe of students named <code>students_df</code>:

<code>students_df</code> table

<table>
<thead>
<tr>
<th>name</th>
<th>age</th>
<th>favorite_color</th>
<th>grade</th>
</tr>
</thead>

<tbody>
<tr>
<td>Tim Voss</td>
<td>19</td>
<td>red</td>
<td>91</td>
</tr>

<tr>
<td>Nicole Johnson</td>
<td>20</td>
<td>yellow</td>
<td>95</td>
</tr>

<tr>
<td>Elsa Williams</td>
<td>21</td>
<td>green</td>
<td>82</td>
</tr>

<tr>
<td>John James</td>
<td>20</td>
<td>blue</td>
<td>75</td>
</tr>

<tr>
<td>Catherine Jones</td>
<td>23</td>
<td>green</td>
<td>93</td>
</tr>
</tbody>
</table>
Write a function named <code>grades_colors</code> to select only the rows where the student’s favorite color is green or red and their grade is above 90.

Example:

Input:

<pre tabindex="0" class="chroma"><code>import pandas as pd

students = {&#34;name&#34; : [&#34;Tim Voss&#34;, &#34;Nicole Johnson&#34;, &#34;Elsa Williams&#34;, &#34;John James&#34;, &#34;Catherine Jones&#34;], &#34;age&#34; : [19, 20, 21, 20, 23], &#34;favorite_color&#34; : [&#34;red&#34;, &#34;yellow&#34;, &#34;green&#34;, &#34;blue&#34;, &#34;green&#34;], &#34;grade&#34; : [91, 95, 82, 75, 93]}

students_df = pd.DataFrame(students)
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>def grades_colors(students_df) -&gt;
</code></pre>

<table>
<thead>
<tr>
<th>name</th>
<th>age</th>
<th>favorite_color</th>
<th>grade</th>
</tr>
</thead>

<tbody>
<tr>
<td>Tim Voss</td>
<td>19</td>
<td>red</td>
<td>91</td>
</tr>

<tr>
<td>Catherine Jones</td>
<td>23</td>
<td>green</td>
<td>93</td>
</tr>
</tbody>
</table>

Write a function to select only the rows where the student's favorite color is green or red and their grade is above 90.

Good Grades and Favorite Colors

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

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.

How would you set up this test?

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.

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

You are a data scientist at YouTube focused on creators.

A PM comes to you worried that amateur video creators could do well before but now it seems like only “superstars” do well.

What data points and metrics would you look at to decide if this is true or not?

Amateur Performance

Product Sense & Metrics

Given that $X$ and $Y$ are independent random variables with normal distributions, what is the mean and variance of the distribution of $2X - Y$ when the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$?

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the mean of the distribution of $2X - Y$?

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the mean of the distribution of $2X - Y$?

Distribution of 2X - Y I

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the variance of the distribution of $2X - Y$?

Given that $X$ and $Y$ are independent random variables with normal distributions, and the corresponding distributions are $X\sim \mathcal{N}(3, 4)$ and $Y \sim \mathcal{N}(1, 4)$, what is the variance of the distribution of $2X - Y$?

Distribution of 2X - Y II

Distribution of 2X - Y

Let’s say that there are six people trying to divide up into two equally separate teams. Because they want to pick random teams, on each round, each person shows their hand in either a face-up or face-down position. If there are three of each position, then they’ll split into teams. 

What’s the expected number of rounds that everyone will have to pick a hand side before they split into teams?

Estimated Rounds

Let’s say you’re interning at a fintech startup that’s building a platform for online games of chance. During testing, one of your simulations flips a coin 10 times and gets 8 tails and 2 heads.

How would you determine if the coin is fair, and what statistical approach would you use to support your conclusion?

How would you assess if a coin is fair after observing 8 tails in 10 flips?

Fair Coin

You are given a binary tree of unique positive numbers. Each node in the binary tree is represented as a dictionary with the following keys:

<ul>
<li><code>data</code>: integer value stored in the node</li>
<li><code>left</code>: reference to the left child (or <code>None</code>)</li>
<li><code>right</code>: reference to the right child (or <code>None</code>)</li>
</ul>

<pre tabindex="0" class="chroma"><code>node = {
 &#34;data&#34;: 6,
 &#34;left&#34;: {
 &#34;data&#34;: 3,
 &#34;left&#34;: {...},
 &#34;right&#34;: {...}
 },
 &#34;right&#34;: {
 &#34;data&#34;: 9,
 &#34;left&#34;: {...},
 &#34;right&#34;: {...}
 }
}
</code></pre>

Given two node values as input (<code>value1</code> and <code>value2</code>), write a function to return the value of the nearest common ancestor (lowest node in the tree that has both nodes as descendants).

Note: If one of the nodes doesn’t exist in the tree, return <code>-1</code>.

Example:

Input:

<pre tabindex="0" class="chroma"><code># Diagram of the binary tree
&#39;&#39;&#39;
 6 
 / \ 
 3 9 
 / \
 2 11
 / \
 5 8
&#39;&#39;&#39;
value1 = 8
value2 = 2
</code></pre>

Output:

<pre tabindex="0" class="chroma"><code>common_ancestor(root,value1,value2) -&gt; 3
</code></pre>

Explanation:

<ul>
<li>Ancestors of <code>8</code>: <code>11 → 3 → 6</code></li>
<li>Ancestors of <code>2</code>: <code>3 → 6</code></li>
<li>Common ancestors: <code>3</code> and <code>6</code></li>
<li>The nearest common ancestor is <code>3</code>.</li>
</ul>

Write a function to return the value of the nearest node that is a parent to both nodes.

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