Let x be a continuous random variable. Prove var(x) . (assuming var(x) exist)

Question

Question

Let x be a continuous random variable. Prove var(x) $\geq 0$ . (assuming var(x) exist)

Answer 1

Answer #1

et x be a cont inuous random variable.

Let pdf of x at be fr)

E(x) f() da JTER

(r E(x))2 dr var (x)E [x- E(x)] JrER

x E(x))20 eR (r- E(x)) dr 20 VrER var(x) 0 ER JrER 11

Answer 2

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