2. This question refers to the random variables X and Y from Question 1. Use your calculated values from that question while answering this question. (a) Let Z=X-aY, where a is a constant to be specified. There is one value of a for which Y and Z are uncorrelated. Find this value of a. [3 marks] (b) Let W=Y+bX, where b is a constant to be specified. There is one value of b for which X and W are uncorrelated. Find this value of b. [3 marks] Show Transcribed Text 1. The random variables X, Y have joint p.m.f. 0.1 ifr=1, y = 4, 0.3 if x = 1, y = 5, 0.1 if x = 4, y = 4, fxy(x,y)=0.1 if z = 4, y = 5, 0.2 if x = 5, y = 4, 0.2 if x = 5, y = 5, 0 otherwise, i.e., Y fxy(x,y) 4 5 1 0.1 0.3 4 0.1 0.1 5 0.2 0.2 X