. Suppose X and Y are two independent random variables with the following probability distributions; 37:2 1 o 1 and Y=y _1 c 1 P[X=a:} {1.30 0.40 can P{Y=y} {1.40 use {1.40 The random variables 3 and T are dened as: S=XE+Y2 and T=X+Y. [a] Construct the table of the joint probability distribution of S and T. [3 marks} {b} Calculate the following quantities; i. 'v'ar{T). given that E[T} = {L [2 marks} ii. Cov{S, T}. [3 marks} iii. E{S|T = {t}. [4 marks} (o) Are 5 and T uncorrelated? Are 3 and T independent? Justifyr your answers. [3 marks}