Your probability class has 300 students and each student has probability 1/3 of getting an A, independent of any other student. Consider the random variable X, the total number of students get an A.

(a) (5 points) Write the down the PMF of the random variable X.

(b) (10 points) Show that the it is a valid PMF.

(c) (10 points) Derive the expectation and variance of X.

(d) (5 points) Calculate the probability that at least 2 students received an A.