Practice tests · GATE

GATE DA probability and statistics: 5 practice questions

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

In the GATE Data Science and AI (DA) paper, probability and statistics is its own section, and it goes further than the engineering-mathematics version in other papers. After counting and distributions, it reaches the central limit theorem, confidence intervals and hypothesis tests. It is also the foundation for machine learning, so marks and understanding both carry over. The five original questions below move from covariance to tests.

What GATE tests in DA probability and statistics

The GATE 2027 DA syllabus runs from counting through the central limit theorem to confidence intervals and z, t and chi-squared tests. Check the exact list on the official syllabus page. The earlier topics are standard: conditional probability and Bayes' theorem, joint, marginal and conditional distributions, expectation, variance and covariance, and the common discrete and continuous distributions.

For the basic version of these topics as other branches meet them, see probability and statistics for GATE engineering papers. This page concentrates on the inference half. The real DA paper has MCQ, MSQ and NAT; all five below are MCQ.

Practice questions

Question 1

Random variables X and Y have Var(X) = 4, Var(Y) = 9 and Cov(X, Y) = 3. The value of Var(X − Y) is:

• A. 1
• B. 7
• C. 10
• D. 13

Question 2

A random sample of 36 observations from a population with known standard deviation 12 has a sample mean of 50. Using z = 1.96, the 95% confidence interval for the population mean is:

• A. (26.48, 73.52)
• B. (44.12, 55.88)
• C. (46.08, 53.92)
• D. (47.56, 52.44)

Question 3

A process is claimed to have mean 100. A sample of 25 items has mean 104, and the population standard deviation is known to be 10. For a two-sided z-test of H0: μ = 100 at the 5% level (critical value 1.96), the correct conclusion is:

• A. z = 2.0; reject H0
• B. z = 0.4; do not reject H0
• C. z = 2.0; do not reject H0
• D. z = 4.0; reject H0

Question 4

A population has mean 20 and standard deviation 6, and its shape is skewed. For samples of size 36, using the central limit theorem and Φ(1) = 0.8413, the probability that the sample mean exceeds 21 is approximately:

• A. 0.3085
• B. 0.8413
• C. 0.0228
• D. 0.1587

Question 5

A die is rolled 60 times. Faces 1 to 6 appear 8, 12, 10, 11, 9 and 10 times respectively. The chi-squared statistic for testing that the die is fair is:

• A. 10.0
• B. 5.0
• C. 1.0
• D. 0.1

Answers and explanations

1. B. Var(X − Y) = Var(X) + Var(Y) − 2 Cov(X, Y) = 4 + 9 − 6 = 7. The covariance term is subtracted for a difference. Option D (13) is what you get if X and Y are treated as uncorrelated.
2. C. The standard error is σ / √n = 12 / 6 = 2. The margin of error is 1.96 × 2 = 3.92, so the interval is 50 ± 3.92 = (46.08, 53.92). Option A forgets to divide by √n, and option B divides by 4 instead of 6.
3. A. The standard error is 10 / √25 = 2, so z = (104 − 100) / 2 = 2.0. Since |z| = 2.0 exceeds 1.96, H0 is rejected at the 5% level. Option B uses σ instead of the standard error.
4. D. By the CLT the sample mean is approximately normal with mean 20 and standard deviation 6 / √36 = 1. So P(mean > 21) = P(Z > 1) = 1 − Φ(1) = 1 − 0.8413 = 0.1587. The population's skewness does not matter because n = 36 is large enough for the CLT.
5. C. If the die is fair, each face is expected 60 / 6 = 10 times. The statistic is Σ (O − E)² / E = (4 + 4 + 0 + 1 + 1 + 0) / 10 = 10 / 10 = 1.0, with 5 degrees of freedom. Option A forgets to divide by E. A value this small is far below any usual critical value, so there is no evidence of an unfair die.

How to prepare DA probability and statistics

• Build the distribution toolkit first: binomial, Poisson, uniform, exponential and normal with means, variances and when each applies, plus the standard normal table values you may be given.
• Master the variance and covariance rules. Linear combinations, independence versus zero correlation, and conditional expectation appear in both this section and in machine learning.
• Memorise the inference recipe: state H0 and H1, pick the test (z if σ is known, t if not, chi-squared for counts and variances), compute the standard error and the statistic, and compare with the critical value.
• Know the sampling distributions of the sample mean, the sample variance (chi-squared) and the t statistic, with degrees of freedom.
• Practise estimators: the maximum likelihood estimate for Bernoulli, Poisson, exponential and normal parameters, and what "unbiased" means.
• Do mixed sets that start from a story and require you to pick the tool. That is how GATE writes the harder questions.

Pair this page with machine learning and linear algebra, which together make up the maths-heavy half of the DA paper. The GATE Data Science and AI guide covers the full section list and a preparation order.

Take the full topic test on PrepMatic

PrepMatic's topic tests run about 15 questions in 30 minutes, which is a good way to test whether you can pick the right inference tool quickly. The free assessment shows your weakest subjects first.

← All practice tests