STUDY MATERIAL · GATE DA
GATE Probability and Statistics: questions and notes
Probability and Statistics questions from 3 GATE papers (2024–2026) with the official answers, each solved step by step, plus notes for each topic, a formula sheet and practice questions.
- previous-year questions
- 34previous-year questions
- solved step by step
- 34solved step by step
- GATE papers, 2024–2026
- 3GATE papers, 2024–2026
- topics with notes
- 7topics with notes
TOPICS
Seven topics, in the order they are taught
Taken from the official GATE 2027 syllabus. Each topic has notes, the formulas you need, its previous-year questions with the official answers and step-by-step solutions, and practice questions.
Counting, sample spaces and the axioms of probability
This topic covers how to count outcomes (permutations, combinations, arrangements with repeated objects, stars and bars, onto functions, inclusion-exclusion) and the formal language of probability: sample spaces, events, the three axioms and the rules derived from them.
5 previous-year questions · 6 marks · 5 practice questions
Conditional, marginal and joint probability, and Bayes' theorem
Conditional probability measures how likely an event is once you know another has occurred.
3 previous-year questions · 5 marks · 4 practice questions
Mean, median, mode, standard deviation, covariance and correlation
This topic covers the summary measures of a data set (centre and spread) and of a pair of variables (covariance and correlation).
4 previous-year questions · 7 marks · 5 practice questions
Random variables, expectation and variance, including conditional expectation
A random variable turns the outcome of an experiment into a number, and its distribution (PMF, PDF or CDF) tells you how probability is spread over those numbers.
8 previous-year questions · 14 marks · 5 practice questions
Discrete distributions: uniform, Bernoulli and binomial
The discrete uniform, Bernoulli and binomial distributions model, in turn, one equally likely choice among n consecutive integers, a single yes/no trial, and the number of successes in n independent identical trials.
2 previous-year questions · 4 marks · 5 practice questions
Continuous random variables and the named distributions: exponential, Poisson, normal, t and chi-squared
A continuous random variable is described by a density whose areas are probabilities.
10 previous-year questions · 15 marks · 5 practice questions
Central limit theorem, confidence intervals and hypothesis tests
The sample mean of n independent observations has mean μ and standard deviation σ / √ n, and by the central limit theorem it is approximately normal for large n.
2 previous-year questions · 4 marks · 6 practice questions
QUESTIONS BY TOPIC AND YEAR
34 questions, by topic and year
How many questions each topic had in the DA papers of each year. This shows what was asked, not what will be asked. We placed each question under a topic ourselves; the exam paper does not label topics. Every question links back to its paper.
| Topic | 2024 | 2025 | 2026 | Total |
|---|---|---|---|---|
| Counting & axioms | 1 | 1 | 3 | 5 |
| Conditional & Bayes | 1 | 1 | 1 | 3 |
| Descriptive statistics | 2 | · | 2 | 4 |
| Random variables | 2 | 4 | 2 | 8 |
| Discrete distributions | · | 1 | 1 | 2 |
| Continuous distributions | 3 | 4 | 3 | 10 |
| CLT & tests | · | 1 | 1 | 2 |
All three GATE DA papers are included: 2024 (IISc Bengaluru), 2025 (IIT Roorkee) and 2026 (IIT Guwahati), each with its final answer key.
Probability and Statistics formulas by topic
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THE OFFICIAL SYLLABUS
What each paper lists under Probability and Statistics
From the GATE 2027 syllabus PDF: all of DA Section 1, “Probability and Statistics”. The syllabus prints Poisson in its list of continuous distributions; the notes treat it as the discrete distribution it is.
GATE DA
Counting (permutation and combinations), probability axioms, Sample space, events, independent events, 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 random variables and probability mass functions, uniform, Bernoulli, binomial distribution, Continuous random variables and probability distribution function, uniform, exponential, Poisson, normal, standard normal, t- distribution, chi-squared distributions, cumulative distribution function, Conditional PDF, Central limit theorem, confidence interval, z-test, t-test, chi-squared test.
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