Identify Probability Distributions for Modeling Ad Clicks
Quick Overview
Evaluates probability distribution knowledge for modeling ad clicks. Strong answers map Bernoulli, binomial, Poisson, and related distributions to click data, provide expectation and variance formulas, compute weighted CTR, and explain exponential PDFs versus CLT behavior.
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: Evaluates probability distribution knowledge for modeling ad clicks. Strong answers map Bernoulli, binomial, Poisson, and related distributions to click data, provide expectation and variance formulas, compute weighted CTR, and explain exponential PDFs versus CLT behavior.
Identify Probability Distributions for Modeling Ad Clicks
Meta
Jul 12, 2025, 6:59 PM
mediumData ScientistTechnical ScreenStatistics & Math
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0
Identify Probability Distributions for Modeling Ad Clicks
You are interviewing for a data scientist role on an ads team. The interviewer asks you to demonstrate knowledge of common probability models for clicks, expectations, variances, mixtures, and asymptotic behavior.
Constraints & Assumptions
Treat this as a statistics fundamentals question in an ads context.
State what each distribution models and its core assumptions.
Use formulas, but also explain why the distribution is useful.
Distinguish event-level clicks, counts over impressions, and waiting-time models.
Clarifying Questions to Ask Guidance
Are we modeling a single impression click, clicks out of a fixed number of impressions, click counts over time, or time until a click?
Is the click probability constant or heterogeneous across users and ads?
Are impressions independent, or are there repeated users and correlated exposures?
Part 1 - Name Distributions
Name three probability distributions suitable for modeling ad clicks and state the core assumption of each.
What This Part Should Cover Guidance
Bernoulli for a single click/no-click event.
Binomial for clicks among a fixed number of independent impressions with common click probability.
Poisson for rare click counts over a fixed exposure or time window.
Optional alternatives such as beta-binomial, negative binomial, or exponential waiting time when assumptions differ.
Part 2 - Expectations and Variances
For those distributions, write the expectation and variance formulas.
What This Part Should Cover Guidance
Correct formulas for Bernoulli, binomial, Poisson, and any optional distribution named.
Interpretation in click-through or count terms.
Part 3 - Weighted CTR
If 90% of users are high-intent and 10% are low-intent, each with expected CTR of 0.30, compute the overall expected CTR.
What This Part Should Cover Guidance
Weighted average over user segments.
Recognition that if both groups have the same expected CTR, the overall expected CTR is also 0.30.
Part 4 - Exponential Distribution and Large Samples
Sketch or describe the PDF of an exponential distribution and explain what happens to its shape as sample size becomes very large.
What This Part Should Cover Guidance
Exponential PDF as highest at zero and decaying monotonically.
Difference between the original data distribution and the sampling distribution of the sample mean.
Central Limit Theorem intuition: sample means become approximately normal as sample size grows, even if individual observations are exponential.
What a Strong Answer Covers Guidance
A strong answer maps each distribution to the right click-data setting, states assumptions and formulas, computes mixture expectations correctly, and avoids confusing an exponential distribution with the large-sample distribution of its mean.
Follow-up Questions Guidance
When would binomial assumptions fail for ad clicks?
How would you model overdispersed click counts?
How would repeated exposures to the same user change the model?