(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) Question Four (20 Marks) (a) The m g f of a random variable X is given by (i) What is the p d f of X (ii) 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

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Question: (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

(a) A random variable X has a geometric distribution with parameter p-0.4.

(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

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