In Exercise 11.118, we discuss the random variable counting the number of seniors in a sample of four undergraduate students at a university, given that the proportion of undergraduate students who are seniors is 0.25. Find the mean and standard deviation of this random variable.

Exercise 11.118

Suppose that undergraduate students at a university are equally divided between the four class years (first-year, sophomore, junior, senior) so that the probability of a randomly chosen student being in any one of the years is 0.25. If we randomly select four students, give the probability function for each value of the random variable X = the number of seniors in the four students.