ML & Data Science Interviews · Statistics & Probability · Lesson 1 of 3
Distributions & the Central Limit Theorem
A few distributions and one theorem underpin most DS statistics questions. Know their shape and when they appear.
- Normal (Gaussian): symmetric bell; sums/averages of many effects. Described by mean and variance.
- Bernoulli / Binomial: single yes/no trial, and the count of successes over n trials (conversions, clicks).
- Poisson: counts of rare events per fixed interval (arrivals, failures).
- Exponential / Uniform / Long-tailed: waiting times, flat priors, and heavy tails (income, traffic) where the mean misleads.
Why the CLT mattersThe Central Limit Theorem: the distribution of the sample mean approaches normal as n grows, regardless of the population's shape (given finite variance). That's why we can put confidence intervals and t-tests on messy real-world data — we're reasoning about the mean, not the raw values.
◆ Lock it in
- Match the distribution to the data: binomial for conversions, Poisson for counts, normal for averages.
- The CLT: sample means tend to normal as n grows, whatever the population shape.
- For heavy-tailed data, the mean can mislead — consider medians/percentiles.
Feynman drill — say it out loudState the Central Limit Theorem and explain why it justifies using t-tests on non-normal data.
Step 1 rate your confidence · Step 2 pick your answer
The Central Limit Theorem says that as sample size grows, what becomes approximately normal?
Step 1 — how sure are you?