(a) A random variable X has a geometric distribution with parameter p-0.4. (i) Find the mean and variance of X. (ii) What is the m.g.f of X? (iii) Find P(X 2) (7 Marks) (b) If X has a poisson distribution so that 3P(X-1)-P(X-2). find P(X-4) (5 Marks) (e) A random variable X has a negative binomial distribution with parameters p=0.6 and r-3 (i) What is the p.d.f of X? (ii) Find the mean, variance and m.g.f of X. (iii) Find P(X 3) (iii) Find E(X) and Var(X) (8 Marks) (8 Marks (b) A sample of size 4 is taken from a box containing 15 articles. It is known that 5 of the articles are defective. Let X be the number of defective articles in the sample. (i) Write the p.d.f of X. (ii) Find the mean and variance of X. (iii) Find P(X-2) (12 Mai