∑GATE DA Atlas
GATE DA / Section 1

Probability and Statistics

Counting, axioms of probability, conditional probability and Bayes' theorem, descriptive statistics, random variables and their distributions, the central limit theorem, confidence intervals and hypothesis tests (z, t, chi-squared).

9 topics88 practice questions≈ 15–18 marksPractise this section →

Probability and Statistics is consistently one of the two heaviest sections of the DA paper (third-party analyses put it at roughly 16 marks in 2024 and 18 in 2025). It is also the foundation for Machine Learning (naive Bayes, LDA, logistic regression) and for the reasoning-under-uncertainty part of AI, so time spent here pays off three times.

What the syllabus lists: counting (permutations and combinations), probability axioms, sample space, events, independent and mutually exclusive events, marginal, conditional and joint probability, Bayes' theorem, conditional expectation and variance, mean, median, mode and standard deviation, correlation and covariance, random variables (discrete with PMFs, continuous with PDFs and CDFs), the uniform, Bernoulli, binomial, exponential, Poisson, normal, standard normal, t and chi-squared distributions, conditional PDFs, the central limit theorem, confidence intervals, and the z-, t- and chi-squared tests.

Topics

Read in order — later topics build on earlier ones
01Counting — Permutations and CombinationsThe sum and product rules, permutations (with and without repetition, of multisets, circular), combinations, stars and bars, the binomial and multinomial theorems, inclusion–exclusion, derangements and the pigeonhole principle — the toolkit for every "equally likely outcomes" probability question.0/10 solved02Sample Spaces, Axioms, Conditional and Joint ProbabilitySample spaces and events, the Kolmogorov axioms and everything that follows from them, joint, marginal and conditional probability, the multiplication rule, independence (pairwise vs mutual), and why "mutually exclusive" and "independent" are almost opposites.0/10 solved03Total Probability and Bayes' TheoremThe law of total probability, Bayes' theorem with priors, likelihoods and posteriors, tree diagrams, the odds form and likelihood ratios, the base-rate fallacy, sequential updating, and the MAP/ML decision rules that machine learning builds on.0/9 solved04Descriptive Statistics — Mean, Median, Mode, Spread, Covariance and CorrelationMeasures of central tendency and spread for raw and grouped data, population vs sample variance, the effect of shifting and scaling, quartiles and skewness, covariance and Pearson correlation with their properties, and why uncorrelated does not mean independent.0/9 solved05Random Variables, Expectation, Joint and Conditional DistributionsDiscrete and continuous random variables, PMFs, PDFs and CDFs, expectation and the law of the unconscious statistician, variance and moments, functions of random variables, joint, marginal and conditional distributions (including conditional PDFs), independence, conditional expectation and variance with the laws of total expectation and total variance, and the Markov and Chebyshev inequalities.0/10 solved06Discrete Distributions — Uniform, Bernoulli, Binomial, Poisson and FriendsThe discrete uniform, Bernoulli, binomial, Poisson, geometric, negative binomial and hypergeometric distributions — when each arises, their PMFs, means, variances and MGFs, the Poisson approximation to the binomial, memorylessness, and how to recognise which model a word problem is describing.0/10 solved07Continuous Distributions — Uniform, Exponential, Normal, t and Chi-squaredThe continuous uniform and exponential distributions, the normal and standard normal with z-scores and the values of Φ you must memorise, the normal approximation to the binomial, and the sampling distributions chi-squared and Student's t — how they are built from normals, their shapes, means and variances.0/10 solved08Sampling Distributions, the Central Limit Theorem and Confidence IntervalsStatistics vs parameters, the sampling distribution of the mean, the law of large numbers, the central limit theorem and when it applies, point estimators (unbiasedness, MLE), and confidence intervals for a mean with known or unknown σ, for a proportion and for a variance — plus how to choose a sample size and how to interpret an interval correctly.0/10 solved09Hypothesis Testing — z-test, t-test and Chi-squared TestsThe logic of significance tests, null and alternative hypotheses, test statistics, critical regions and p-values, Type I and Type II errors and power, one- vs two-tailed tests, and the z-test, t-tests (one-sample, paired, two-sample) and chi-squared tests (goodness of fit, independence, variance) with a decision table for choosing among them.0/10 solved