Discussion Forum



1)

 The p.d.f  of c.r.v X is given by  $f(x)=\frac{x+2}{18}$  , if -2 < x < 4=0, otherwise =0, then P[|x| <1]=


A) $\frac{2}{9}$

B) $\frac{4}{9}$

C) $\frac{1}{9}$

D) $\frac{1}{18}$

Answer:

Option A

Explanation:

$f(x)=\begin{cases}\frac{x+2}{18}, & -2<x<4 = 0\\0 & otherwise\end{cases}$

$P[|x| <1]=\int_{-1}^{1 }f(x) dx$

 $=\int_{-1}^{1 }\left(\frac{x+2}{18}\right)dx=\frac{1}{18}\left[\frac{x^{2}}{2}+2x\right]^{1}_{-1}$

$=\frac{1}{18}\left[\left(\frac{1}{2}+2\right)-\left(\frac{1}{2}-2\right)\right]=\frac{4}{18}=\frac{2}{9}$