Question $2$: $($You need to do research on this question.$)$

$($a$)$ Define the exponential random variable and explain briefly. $(10$ P$)$

$($b$)$ Assume that the length of phone calls made at a particular telephone booth is exponentially

distributed with a mean of $3$ minutes. If you arrive at the telephone booth just as someone was about

to make a call, find the probability that you wait more than $5$ minutes. $($Use the exponential random

variable.$)(15$ P$)$