(a) Let X be a discrete random variable with the following cumulative distribution function: x < 0 ܘ ܝܗ ܢܬܙܗ F(x) = 0

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(a) Let X be a discrete random variable with the following cumulative distribution function: x < 0 ܘ ܝܗ ܢܬܙܗ F(x) = 0<x< 2 2<x< 4 < x>4 . 1. Determine the probability mass function of X. (6 marks) (b) Let X, Y be two continuous random variable with joint probability density function f(x,y) = cx?y(1+y) for 0<x<3 and 0 Sy<3, and f(x,y) = 0 otherwise. i. Find the value of c. (4 marks) ii. Compute the joint probability P({1 < X <2} n{O <Y <1}). (4 marks) iii. Determine the joint cumulative distribution function of X and Y. (4 marks) iv. Determine the marginal probability density function of X. (4 marks) v. Are X and Y independent? (4 marks)