Pls kindly hlp with my hw. I need it ASAP. Your help will be very much appreciated. Thanks

2. (a) Let X be a discrete random variable with probability: x) : E for a: : 1,2,3,4 (i) Find the Moment Generating Function (MHGF) of X. [2 marks] (ii) Find E(X), using differentiation of the M.G.F. [2 marks] (iii) Find Var(X), using differentiation of the M.G.F. [2 marks] P. 1 of 5 MA2506 Probability 85 Statistics - Final exam (b) A discrete random variable X has moment generating function: 1 fotl : % [(3 _|_ e't)2 + (37* +et)2] (i) Write down the probability distribution function of X for all possible values of :5. [4 marks] (ii) Find the mean and variance of X. [2 marks] (0) Let X be a random variable with p.d.f. given by: x) : 65\" for 3: > 0 Derive the Moment Generating Function (MGmF) Show All necessary steps, including lim :1: > 00. [5 marks]