(Solved): Suppose the university is looking for 30 student representatives to serve on a variety of committee ...

Suppose the university is looking for 30 student representatives to serve on a variety of committees across campus. They plan to randomly select current students one at a time and send them an invitation. Suppose $75\%$ of students will agree to serve on a committee if invited. Let $Y$ be the number of students the university will need to invite to recruit their target number of student representatives. [Note: Since the number of students at the university is so large compared to the number of students they are looking for to serve on university committees, you may assume that sampling is done with replacement for this question.] (a) (4 marks) What probability distribution may be an appropriate model of $Y$ ? Justify your answer. 3(a)ANSWER : (b) (3 marks) Find (i) $E(Y)$, and (ii) $P(Y\le a)$ where $a=E(Y)$. Justify your answer. * 3(b) ANSWER (c) (3 marks) Write $\mathrm{R}$ code to simulate 1000 repetitions of the random experiment described in this question. Save your simulated observations in an $\mathrm{R}$ vector called invitations and obtain of histogram of your simulated values. Comment your code to describe your step(s). \# 3(c) ANSWER: \# set seed with your student number (d) (4 marks) Estimate $E(Y)$ and $P(Y\le a)$ where $a=E(Y)$ using the generated random observations in Sc. Comment your code to describe your step(s). Are they close to the theoretical values you determined in part $3b$ ? Why or why not. \# 3(d) ANSWER: