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a) Let X1 and X2 have a joint probability density function given by: _ 3x1, 0 5x25111514 f(x1. 12) _ { 0, elsewhere Find the covariance of X1 and X2. (7 marks) b) If the continuous random variable X has the probability density function _ k-e'g", forx>0 f(x) _ { 0, elsewhere (i) Find k so that f (x) can serve as the probability density function of the continuous random variable X. (5 marks) (ii) Compute P(0.5 S X S 1). (5 marks) 0) If X is a Poisson distributed random variable with mean 1, nd the moment-generating function 1310:) of X. (8 marks)