Tech_Interview_Prep

Probability Distributions

The handful of named distributions (normal, binomial, Poisson) that show up repeatedly, and what each models.

OverviewQ&AMCQ

Try answering in your head first, then click a question to check the model answer.

Q1.Why is the Central Limit Theorem so foundational to statistical inference?(show answer)

It guarantees that the sampling distribution of the mean approaches Normal as sample size grows, regardless of the underlying population's distribution shape. This is what justifies using Normal-based confidence intervals and hypothesis tests (like the t-test) even when the raw data itself isn't normally distributed, as long as the sample size is reasonably large.

Q2.When would you model a variable with a Poisson distribution instead of a Binomial one?(show answer)

Binomial requires a fixed, known number of discrete trials (e.g. 100 coin flips). Poisson models the count of independent events in a continuous interval where there's no natural fixed "number of trials" — e.g. number of customer support tickets per hour, or website errors per day — where events could in principle happen any number of times.

Q3.What are the two parameters that fully define a Normal distribution, and what does each control?(show answer)

The mean (μ) controls the center/location of the distribution — where its peak sits. The standard deviation (σ) controls the spread — how wide or narrow the bell curve is. Together they fully determine the distribution's shape; two Normal distributions with the same μ and σ are identical.

Q4.Why might you choose a log-normal distribution to model something like income or stock prices instead of a Normal distribution?(show answer)

Income and prices are strictly positive and often right-skewed (a long tail of high values), which a symmetric Normal distribution can't represent well and would allow (invalidly) negative values. A log-normal distribution — where the log of the variable is normally distributed — naturally stays positive and captures that right-skew, matching how such data actually tends to behave.