Question

If $r. v. x :$ waiting time in minutes for bus and $p.d.f.$ of $x$ is given by $f(x) = \begin{cases} \frac{1}{5} , & 0\le x\le5 \\\[2ex] 0, & \text{otherwise} \end{cases}$ 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)

$0.8$

Answer 2

Given, f(x) = \begin{cases} \frac{1}{5}, & \text{ 0 \leq ,x \leq ,4 } \\\[2ex] 0, & \text{ otherwise } \end{cases}
$\therefore P(0 \leq x \leq 4) =\int\limits_{0}^{4} f(x) d x$
$=\int\limits_{0}^{4} \frac{1}{5} d x=\frac{1}{5}[x]_{0}^{4}$
$=\frac{1}{5}(4-0)=\frac{4}{5}=0.8$