GATE Probability and Statistics: Conditional expectation and variance – Previous Year Questions

4 GATE previous year questions on Conditional expectation and variance (Probability and Statistics, Data Science and Artificial Intelligence) with answers and explanations, from every paper.

1. GATE 2024 DA Q36 (2 marks, Multiple choice) – A fair six-sided die (with faces numbered 1, 2, 3, 4, 5, 6) is repeatedly thrown independently. What is the expected number of times the die is thrown…
2. GATE 2024 DA Q59 (2 marks, Numerical answer) – Consider a joint probability density function of two random variables X and Y: f X,Y(x, y) = cases 2xy, & 0 < x < 2,\ 0 < y < x \\ 0, & otherwise…
3. GATE 2025 DA Q11 (1 mark, Multiple choice) – Suppose X and Y are random variables. The conditional expectation of X given Y is denoted by E[X Y]. Then E[E[X Y]] equals
4. GATE 2026 DA Q44 (2 marks, Multiple choice) – Let X and Y be two independent random variables. X follows Bernoulli(p = 0.3) distribution and Y follows Normal( = 0, 2 = 100) distribution. Which of…