### Problem 1 Let $X$ denote the checkout time (in minutes) of a customer in a Grocery store. Assume SX$ is a random variable uniformly distributed between $10$ and $20$ minutes, i.e., $X sim Unif(10, 20)$. [Use R code * *only** for part e] a) Write down the probability density function (pdf) of $X$, by replacing the two question marks (?) with appropriate values. $$ f(x) = \\begin{cases} ? & mbox{ for } 10 \\le x \\le 20, \\\\ ? & mbox{ for } x 20. end{cases } $$ f( z ) = for 10 20. b) what is the expected checkout time? c) what is the first quartile ($Q_1$) of checkout times? show your calculations. d) what is the chance that a randomly selected customer at that store will have to wait more than $15$ minutes? Show your calculations. e) Now answer the same question as in d) using R function punif in a code chunk below (Type `?punif in the R console to know more about this function) . Make sure to set echo=TRUE and eval=TRUE at the start of your code chunk