Calculate Expected Impressions and Probability for Users
MetaData Scientist · Onsite
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Meta probability question on random ad-impression allocation, including binomial expectation, probability a user sees at least one impression, expected unique reach, and large-population approximations.
Scenario
Randomly allocating Y ad impressions to X users
Question
Given X users and Y impressions assigned uniformly at random, 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?
Hints
Model each assignment as Bernoulli with p = 1⁄X, then apply binomial expectation, complement rule, and linearity.
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