Distributions preview

SciPy names distributions consistently: stats.norm, stats.t, stats.chi2, stats.binom, etc. Each supports pdf/cdf/ppf and random sampling for simulation and inference.

Common distributions

• norm — Gaussian (continuous)
• t — Student's t (small-sample inference)
• chi2 — chi-squared (goodness of fit, variance tests)
• binom, poisson — discrete counts
• uniform, expon — modeling and simulation

Fitting and comparing

Use stats.fit (newer API) or manual MLE with curve_fit for custom models. Compare empirical histograms to theoretical pdf for sanity checks.

Examples

import numpy as np
from scipy import stats

print('binom P(X=3):', stats.binom.pmf(3, n=10, p=0.3))
print('t 95% critical (df=9):', stats.t.ppf(0.975, df=9))

Important interview questions and answers

1. Q: pdf vs pmf?
   A: pdf for continuous density; pmf for discrete probability mass at integer k.
2. Q: loc and scale?
   A: Location and scale parameters—mean and std for normal; generalize to other families.

Self-check

1. Give pdf vs pmf use cases.
2. What does ppf return for norm?

Pitfall: Use pmf for discrete counts (binom) and pdf for continuous (norm)—mixing them is a common exam mistake.