Random variables.
From mass to density.

Oct 19, 2026 · @Rajat Goel

Roadmap #

This guide covers Module 1 of an 8-module plan that follows the GATE DA Probability & Statistics syllabus, not the much broader GATE Statistics (ST) paper.

• Random variables — foundations (this guide): sample space, random variable, PMF, CDF, interval probabilities
• Expectation and variance: mean, median, mode, E[g(X)], variance, standard deviation
• Discrete distributions: discrete uniform, Bernoulli, binomial, Poisson
• Continuous distributions: continuous uniform, exponential, normal, standard normal
• t and chi-squared distributions: degrees of freedom, shapes, links to the normal
• Multiple random variables: joint, marginal, conditional distributions; independence; covariance, correlation
• Central Limit Theorem: sums and averages, normal approximation
• Statistical inference: confidence intervals, z-, t- and chi-squared tests

Counting, conditional probability and Bayes' theorem come in as prerequisites wherever needed.

Syllabus trap: the DA syllabus lists Poisson among the continuous distributions. Poisson is discrete — it counts events (0, 1, 2, …). Answer exam questions by the mathematics, not by where the syllabus lists it.