The MGF factors, proving independence. X~N(0,1) and Y~Gamma(shape3,scale2). Thus E X²=1 and E(1/Y)=1/[(3−1)2]=1/4. The requested expectation is 6×1×1/4=**1.50**.
More Functions of Random Vectors questions
GATE 2023 ST Q53– X has density e(−x) for x≥0,zero otherwise. Which hold? U(a,b) denotes the uniform law on…
GATE 2023 ST Q55– U,V are iid with density λ²x e(−λx),x>0,λ>0. Which statements hold?
GATE 2021 ST Q42– X∼Uniform[−π/2,π/2]. Which statement is NOT true?
GATE 2026 ST Q63– Independent U₁,U₂,U₃ are exponential with respective rates 1,2,3. Let…