Question

Find mean and variance of a random variable whose probability density function is given by

f(x) = C(x + 1) when -1<= x <=1 otherwise f(x) = 0

Find C values also.

Answer 1

variable x is The prokoboilika deasita functions sgiven f(x2= {((x+1) ; -1<x</ Otherwise o'

We know thad? S fox, de = 1 -1 cf + 1) dx = 1 -1 C le tx -| 9 [6+1)-(8-27-1 c ( 3 + 1 - 2 + 1] = 1 -> - 2 c = 1 C c=1 2

Then the pay of xas, f(x)= . -/<x</ i Olheroise xt! {(x): Sagrert -| == Sarcasnode = ± l'arxid 3 2 + x2 - = t 1 2 3 (( Ź (3) )-6*+5 ch

E (A?l= (xrfoods - = 4 Saxondse *S62722) de = 14 3 7 3 -1 = 2 3 á (3) = OL

Then var(x) = E(X22 - [E(x)] 2 2 a 3 3- 1 9. 2 Na Hences Mean of a X, E(X)= Variance of Xn Vara) = 2 2