my #3 Please, write clearly and justify all your steps, to get proper credit for your work. [1] Suppose that the probability density function r] of the length X of an international phone call, rounded up to the next minute, is given by: ----u [a] Calculate PIX E 2},P[X a: 2], and PEX 3 1]. [b] Plot the cumulative distribution function FLT]. [c] Calculate the mean a = E[X]. [d] Calculate 1ng) and us it to compute the variance 02. [2] A job applicant to a company is required to submit one, two, three, four, or ve forms depending on the nature of the job. Let X to denote the number of forms required of an applicant. The probability that .1: forms are required is lmown to be proportional to .r, that is, p{r}=kr, forr=1,2,...,5. [a Calculate the value ls: so that 33(3) is a probability mass function. J [b] What is the probability that at least 2 forms are needed? [c] What is the probability that at most 2 forms are needed? [d] Calculate EU?) and us it to compute the variance on. [3] This problem requires H: follon.r the instruction on the class webpage to install Rstudio. Using the data of Problem {I}, use R to do the following. [a] Plot the probability mass flmction. Remember to label the x and y axes. [b] Verify that the values of the probability add up to 1. [c] Plot the cumulative distribution function. Remember to label the x and y axes. NOTE: I 1will ask to attach your plots and your R scripts to your Quiz