Calculate Expected Impressions and Probability for Users

Q: Calculate Expected Impressions and Probability for Users

This question evaluates understanding of basic probability theory and expectation in random allocation (occupancy) scenarios, assessing competency in modeling event probabilities and aggregate expected counts for distinct users.

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Question

Random Allocation of Y Ad Impressions to X Users

Setup (assumptions)

There are X distinct users and Y ad impressions.
Each impression is assigned independently and uniformly at random to one of the X users (users may receive multiple impressions).

Questions

What is the expected number of impressions a particular user receives?
What is the probability that a specific user sees at least one impression?
What is the expected number of users who see at least one impression?

Calculate Expected Impressions and Probability for Users

Random Allocation of Y Ad Impressions to X Users

Setup (assumptions)

Questions

Solution

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