QUESTION FOUR
(a) A committee of five 7 person is to be selected randomly from a group of 7 men and 12
women. Find the probability that the committee.
(i) Consists of 4 men and 3 women.
(ii) Consists of men.
(b) A continuous random variable X has a probability density function fX(x) = k(2 − x) if
0 < x < 1, where k is a positive constant.
(i) Find the value of k.
(ii) Find the expectation of the random variable X
(iii) Find the P(X ≤ 0.65).
(c) Give that the random variable X is uniformly distributed over the interval [−α, α],
where α> 1. Find the value of α if P(X < 1
2
) = 0.7
