It is requested that plz solve the question neatly as it is for my online assignment and it holds great assessment..

I will be at your debt...

Q1 Suppose that the random variables X and Y' are independent, and both of them are uniformly distributed on the interval (0, a], a > 0. That is, the probability density functions of X and Y are given, respectively, by fx(x) = 1/a, 0, OSISa otherwise, and fr(y) = 1/a, Osysa, 0, otherwise. (a) Find the joint probability density function fxy(r, y) of X and Y. (5 marks] (b) Let Z = . Identify the distribution function Fz(=) and the proba- bility density function fz(=) of Z. [15 marks] Q2 Suppose that X, Y are continuous random variables with joint density func- tion fx.y(x,y) = y>0, -y 0. [4 marks] (c) For each of these two distributions, give the standard name of the distribution, specifying any parameter values. [2 marks] (d) Find E[X] and E[Y]. [4 marks] (e) Find E[XY] and hence find the covariance Cov[X, Y]. [4 marks] (f) Are X and Y independent? [3 marks]