Stats & Probability

Inverting conditional probabilities: $P(H \mid E) = P(E \mid H)P(H)/P(E)$ — and why ignoring the prior (base rate) is the single most common probability error in interviews and in production

Bernoulli, binomial, Poisson, normal, and exponential — what data-generating story each one tells, and how to recognize which one an interview question is secretly about

Pick the parameter value that makes the observed data most probable — the single principle behind sample means, logistic regression, and cross-entropy loss

Estimate the sampling distribution of any statistic by resampling your own data with replacement — standard errors and confidence intervals without formulas, for medians, ratios, and other formula-less statistics

A statistic computed from a random sample is itself a random variable; the CLT says the sample mean is approximately normal with standard error $\sigma/\sqrt{n}$ — the engine behind nearly every test and interval

Estimate $\pm$ margin: the range of parameter values compatible with the data, built from the standard error — and what the 95% actually refers to (the procedure, not this interval)

What a p-value actually is — $P(\text{data this extreme} \mid H_0)$ — the standard test recipe, and the misinterpretation traps interviewers are really probing for

Peeking, multiple testing, sample ratio mismatch, and novelty effects — the four standard ways a correctly-computed p-value still lies to you, and the checks that catch each one

Why observed associations routinely reverse under intervention — confounders, Simpson's paradox with real numbers, and the ladder of methods (randomization first) for earning a causal claim

Power, MDE, and the sample-size calculation: $n \approx 16\sigma^2/\delta^2$ per arm — how to size an A/B test before launch instead of explaining an inconclusive one after