Random variables and standard distributions: previous year questions

Asked 5 times in 2 exams across 3 years. Newest first.

Practise Random variables and standard distributions, easy to hard →

1. GATE 2023 Q62Let X be a random variable with the probability density function f(x) such that f(x) = { 1/2√3 if -√3 < x < √3; 0 otherwise } Then, the variance of…
2. IIT JAM 2022 Q31Let X ~ N(μ_X, σ_X²) and Y ~ N(μ_Y, σ_Y²). Which of the following is/are NOT correct?
3. GATE 2021 Q40Consider that a sample of size 3 is randomly drawn from a population that takes only two values, equally likely: -1 and 1. Let z=max (x₁,x₂,x₃)…
4. IIT JAM 2021 Q23X and Y are independent with F_X(x) = 1 - (3/4)^x and G_Y(y) = 1 - (2/3)^y for x, y = 1, 2, 3, …. Let Z = min {X, Y}. Then P(Z ≥ 6) is
5. IIT JAM 2021 Q57Let X₁, X₂, X₃, X₄ be independent standard normal variables and Y = (X₁ + X₂)² + (X₃ + X₄)². The variance of Y equals _ (in integer).