Identify Probability Distributions for Modeling Ad Clicks
Company: Meta
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
##### Scenario
Ads team wants to understand click behaviour and validate statistical knowledge during an analytical-execution round.
##### Question
Name three probability distributions suitable for modeling ad clicks and state the core assumption of each. Write the expectation and variance formula for those distributions. If 90 % of users are high-intent and 10 % are low-intent, each with an expected click-through of 0.30, compute the overall expected CTR. Sketch the PDF of an exponential distribution and describe what happens to its shape as sample size becomes very large.
##### Hints
Think Bernoulli, Binomial, Poisson, Exponential; use law of total expectation; recall CLT.
Quick Answer: This question evaluates a data scientist's mastery of probability modeling for binary and count data, computation of expectation and variance, mixture-model reasoning for heterogeneous populations, and understanding of asymptotic sampling behavior (central limit theorem) within the Statistics & Math domain.