Question One (30 Marks) (a) The p.d.f of a random variable X is given by, f(x)=2(1-x).0 (ii) P(X <3) (4 Marks) (i) (ii) (c)

Question One (30 Marks) (a) The p.d.f of a random variable X is given by, f(x)=2(1-x).0 (ii) P(X 2) (5 Marks) (d) In a small pond there are 18 fish, 6 of them have been tagged. If a fisherman's catch consists of 5 fish, selected at random and without replacement, and X denotes the number of tagged fish, find the probability that X is at most 2. (7 Marks) (e) The m.g.f of a random variable X is given by, Find: m(t)=-31+812 (i) P(-5