The p.d.f. of c.r.v. $X$ is given by $f(x)=\frac{x+2}{18}$ if -2

Question

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

Aicharya · Accepted Answer

$\begin{array}{c} f(x)=\frac{x+2}{18}, \quad-2 < x < 4 \ =0, \quad 	ext { otherwise } \ \begin{aligned} P(|x| < 1)=P(-1 < x < 1) &=\int_{-1}^{1} \frac{x+2}{18} \mathrm{dx} \ &=\int_{-1}^{1} f(x) d x=\frac{1}{18}\left[\frac{1}{2}+2-\frac{1}{2}+2ight]=\frac{4}{18}=\frac{2}{9} \end{aligned} \end{array}$

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

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