Calculate Expected Impressions and Probability for Users
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Onsite
##### 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.
Quick Answer: 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.