A statistics adjunct wants to understand how many students in their class will pass. Let X be the number of students in the class who pass. The adjunct has 30 students in total, and the probability that a student passes the class is 0.7. Assume that a student's ability to pass the class is independent of the other students in the class. Answer the following: (a) What is the probability distribtion of X? (b) Compute Pr(X= 10), that is, the probability that exactly 10 students pass the class. (c) Compute Pr(X21), that is, the probability that at least one student passes the class. (d) Compute the expected number of passes E(X) and the variance Var(X).