Solve the following problems.

(a) [1pt] The probability mass function of some random variable X is P(X = x) = x k for x = 1, 2, . . . , 5. What is the constant k?

(b) [1pt] Use the same X as the problem (a). What is P(2 X 4)?

(c) [1pt] There are four students and three teachers. You are going to randomly select three people among them. Let's say Y is the number of the students in your choice of three people. Find all possible values of Y .

(d) [1pt] Use the same Y as the problem (c). What is the probability mass function of Y ? (e) [1pt] Use the same Y as the problem (c). What is P(Y 1)?