Multiply the polynomial by the density. The expectation times 4/3 is (4/13)∫₀¹[x⁵−25x⁴+186x³−405x²+243x]dx. Integrating termwise gives (4/13)[1/6−5+186/4−135+243/2]=26/3≈**8.67**.
More Moments and Inequalities questions
GATE 2026 ST Q17– X has density 4x²e(−2x) for x>0 and zero otherwise. If Y=ln X, which holds?
GATE 2026 ST Q52– X has full support 1,2,3,…, E(X²)<∞ and CDF F. Which hold?
GATE 2024 ST Q39– X has density c₁/√x for 0<x≤1,c₂/x² for x>1,zero otherwise. If P(1/4≤X≤4)=5/8, consider…
GATE 2023 ST Q52– X is positive and continuous with finite mean. Let Y=⌊X⌋. Which hold?
GATE 2022 ST Q27– X i are iid N(1,4),and S n=ΣX i². Find lim as n→∞ of [Var(S n)/n−(E(S n)/n)²],as an…
GATE 2021 ST Q11– X is a nonconstant positive random variable with E X=9. Which holds?