The CDF has a jump of 1/2 at zero and density 1/4 elsewhere on (−1,1). The limiting interval in B includes that atom and length 1/2 of continuous density,giving 1/2+(1/2)(1/4)=5/8. A excludes the atom and tends to 1/8. C is zero for n>1,and D’s atom is 1/2. **B**.
More Random Variables and Transforms questions
GATE 2022 ST Q29– X has density c(x−⌊x⌋) on 0<x<3,zero elsewhere. Find P(X∈[1/2,2]),to two decimals.
GATE 2022 ST Q30– X has MGF M(t),mean 1/2 and variance 1/4. Y has MGF H(t)=[(3/4)e(2t)+1/4]M(t) near zero.…
GATE 2022 ST Q44– I:For a variable with density e(− x )/2 on ℝ,there exist iid X₁,X₂ such that X₁−X₂ has…
GATE 2022 ST Q49– For a>0,suppose P(aX/(2π)∈ℤ)=1. Let φ X(t) be its characteristic function. Which hold?
GATE 2021 ST Q26– X has CDF 0 for x<1,a/2 for 1≤x<2,c/6 for 2≤x<3,and 1 for x≥3. Let A n=[1+1/n,3−1/n] and…
GATE 2021 ST Q57– X has MGF M(t)=(et−1)/[t(1−t)] for t<1,with the continuous value at t=0. Find P(X>1),to…