Let 𝑋 be a continuous random variable such that 𝑃(𝑋 ≥ 0)=... | Statistics | SolveeIt | Solveeit

Today, August 23

Question

Let 𝑋 be a continuous random variable such that 𝑃(𝑋 ≥ 0)=1 and 𝑉𝑎𝑟(𝑋)<∞ . Then, 𝐸(𝑋 2) is

A

$2 ∫^∞_0 𝑥^2 𝑃(𝑋 > 𝑥) 𝑑x$

B

$∫^∞_0 𝑥^2 𝑃(𝑋 > 𝑥) 𝑑x$

C

$2∫^∞_0 𝑥𝑃(𝑋 > 𝑥) 𝑑x$

D

$∫^∞_0 𝑥 𝑃(𝑋 > 𝑥) 𝑑x$

Answer

$2∫^∞_0 𝑥𝑃(𝑋 > 𝑥) 𝑑x$

Explanation

Solution

The correct option is (C): $2∫^∞_0 𝑥𝑃(𝑋 > 𝑥) 𝑑x$