How do I approach Analytics & Experimentation interview questions?

Analytics & Experimentation questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master analytics & experimentation interviews.

What difficulty level is this interview question?

This is a easy difficulty Analytics & Experimentation question, commonly asked during Onsite rounds at Meta.

What role is this question designed for?

This question is commonly asked for Data Scientist candidates at Meta during technical interviews.

Expected impressions per user under random assignment

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of probability and statistical modeling, focusing on expected values, occupancy/assignment distributions, and Poisson approximations in the context of randomized ad impression allocation, placed in the Analytics & Experimentation domain for data science roles.

Random Assignment of Ad Impressions Across Users

Setup

In an A/B experiment, Y ad impressions are served uniformly at random across X distinct users. Each impression is independently assigned to one of the X users; multiple impressions can be delivered to the same user.

Questions

For an arbitrary user i, what is the expected number of impressions they receive?
What is the probability that user i receives at least one impression?
Provide both the exact expressions and the large-scale Poisson approximations.

Solution

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