Question

If r.v$X$: waiting time in minutes for bus and p.d.f of $X$ is given by
$f\left(x\right)=\{\begin{array}{c}\frac{1}{5},0\le x\le 5\\ 0,otherwise\end{array}$
then probability of waiting time not more than $4$ minutes is $=$...........

• A. $0.3$
• B. $0.8$
• C. $0.2$
• D. $0.5$

Answer 1

Answer: (B)

$0.8$

Given :

$f\left(x\right)=\{\begin{array}{c}\frac{1}{5},0\le x\le 5\\ 0,otherwise\end{array}$

Probability of waiting time not more than $4$ is same as probability of waiting time less than $4$ minutes and it is given by

$P(X<4)=P(X=3)+P(X=2)+P(X=1)+P(X=0)$

$=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}$ .... [From the definition of $f$]

$=4\times \frac{1}{5}=0.8$