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Probability

Random Seed Function

You have a function that outputs a random integer between a minimum value, \(N\), and a maximum value, \(M\). Call this function \(X\).

Take the output from the random integer function and place it into another random function as the max value with the same min value \(N\). This second function you can call \(Y\).

<ol>
<li>What would the distribution of the samples look like?</li>

<li>What would be the expected value?</li>
</ol>

Given a function that outputs a random integer between a min value N and a max value M, and then uses the output as the max value for a second function with the same min N, what is the expected value?

Given a function that outputs a random integer between a min value N and a max value M, and then uses the output as the max value for a second function with the same min N, what is the expected value?

Random Seed Function I

What does the Law of Iterated Expectation state for two random variables X and Y?

What does the Law of Iterated Expectation state for two random variables X and Y?

Random Seed Function II

Suppose there exists a new airline named Jetco that flies domestically across North America. Jetco recently had a study commissioned that tested the boarding time of every airline, and it came out that Jetco had the fastest average boarding times of any airline.

What factors could have biased this result, and what would you look into?

What could potentially bias the average boarding time in favor of an airline that only flies domestically?

What could potentially bias the average boarding time in favor of an airline that only flies domestically?

Boarding Times Bias

A new airline came out as the fastest average boarding times compared to other airlines.  What factors could have biased this result and what would you look into?

Statistics

Let’s say you work for a social media company that has just done a launch in a new city. Looking at weekly metrics, you see a slow decrease in the average number of comments per user from January to March in this city.

The company has been consistently growing new users in the city from January to March.

What are some reasons why the average number of comments per user would be decreasing and what metrics would you look into?

What metric could be used to measure if active users are still engaging on the platform despite an overall decrease in the average number of comments per user?

What metric could be used to measure if active users are still engaging on the platform despite an overall decrease in the average number of comments per user?

Decreasing Comments

How would you investigate a decline in the average number of comments per user?

Question	Topic	Difficulty	Ask Chance
Random Seed Function	Probability	Medium	Very High
Boarding Times Bias	Statistics	Medium	Low
Decreasing Comments	Product Sense & Metrics	Easy	Low