GATE Engineering Mathematics: Probability and Statistics – Previous Year Questions

16 GATE previous year questions on Probability and Statistics (Engineering Mathematics, Biomedical Engineering) with answers and explanations, from every paper.

1. GATE 2020 BM Q54 (2 marks, Numerical answer) – A continuous random variable has normalized density f(x)=e-a x for all real x, where a is a real constant. Find its variance to one decimal place.
2. GATE 2020 BM Q57 (2 marks, Numerical answer) – Recorded pairs (age in years,diastolic BP in mmHg) are (23,65),(24,60),(25,62),(26,70),(28,70),(29,73),(31,75),(35,83),(40,90). Using linear…
3. GATE 2021 BM Q11 (1 mark, Multiple choice) – For f X(x)=1qex+e-x to be a valid probability density on the real line, find q.
4. GATE 2021 BM Q58 (2 marks, Numerical answer) – A drug has approval probability 0.95 if tests show no side effects and 0.50 if tests show side effects. A physician assigns probability 0.20 that…
5. GATE 2021 BM Q59 (2 marks, Numerical answer) – Group A has 10 measurements with mean 35 and standard deviation 0.4. Group B has 15 measurements with mean 38 and standard deviation 0.6. Find the…
6. GATE 2022 BM Q32 (1 mark, Numerical answer) – In the source’s simplified model, three family members independently have equally likely positive or negative COVID status. Given that one member has…
7. GATE 2022 BM Q50 (2 marks, Numerical answer) – Six subjects have systolic pressures in mmHg [120,90,100,110,140,130] and corresponding heart weights in grams [500,300,420,390,490,450]. Find the…
8. GATE 2023 BM Q11 (1 mark, Multiple choice) – Find the difference between the mean and median of the dataset 1, 2, 3, 4, 6, 8.
9. GATE 2023 BM Q12 (1 mark, Multiple choice) – For a binomial random variable X, which proposed pair of expectation E(X) and variance Var(X) cannot be true?
10. GATE 2024 BM Q28 (1 mark, Numerical answer) – Four people independently each have infection probability 0.1. Find the probability that at least two are infected, rounded to three decimals.
11. GATE 2024 BM Q29 (1 mark, Numerical answer) – Gaussian noise has mean zero and standard deviation 1 mV. Find P(noise>2 mV or noise<−2 mV) as a percentage, nearest integer.
12. GATE 2025 BM Q33 (1 mark, Multiple choice) – The dataset −5,1,a,5,b is in ascending order and has both mean and median 3. Find b.
13. GATE 2025 BM Q38 (2 marks, Multiple choice) – A binomial variable from N independent trials has expectation 16 and variance 12. Find N.
14. GATE 2026 BM Q16 (1 mark, Multiple choice) – X has mean 3 and standard deviation 2. If Y=(X−3)/4, find the standard deviation of Y.
15. GATE 2026 BM Q21 (1 mark, Multiple choice) – A coin gives heads with probability 1/3 and tails with probability 2/3. X=1 for heads and −1 for tails. Find Var(X).
16. GATE 2026 BM Q53 (2 marks, Multiple select) – Which changes increase statistical power when comparing two sample means using a t-test, with other assumptions fixed?