Identify Probability Distributions for Modeling Ad Clicks

Q: Identify Probability Distributions for Modeling Ad Clicks

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.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Question

Context

You are interviewing for a data scientist role on an ads team. You are asked to demonstrate knowledge of common probability models for clicks, basic expectations, and asymptotic behavior.

Tasks

Name three probability distributions suitable for modeling ad clicks and state the core assumption of each.
For those distributions, write their expectation and variance formulas.
If 90% of users are high-intent and 10% are low-intent, each with an expected click-through rate (CTR) of 0.30, compute the overall expected CTR.
Sketch (describe) the PDF of an exponential distribution and explain what happens to its shape as sample size becomes very large (hint: think about the sampling distribution/CLT).

Identify Probability Distributions for Modeling Ad Clicks

Context

Tasks

Solution

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