(a) The discrete random variable X has moment generating function: Mx (1) = k + } ( P² + P²³ + P³) , where k is a positive constant. (1) Find the value of k. (ii) Determine P (X > 4). (iii) Use Mx (1) to calculate the mean and the variance of X. b) The continuous random variable X has probability density function - {* (1) Find the value of k. (ii) Find the mean of X. (iii) Find the variance of X. f(x)= kx (x-3), 3 < x <4 0, otherwise.

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