statistical questions

Problem 4 {60 marks total] Suppose that: (Y |X = 1:) ~ U(0,4x) X ~ Bera(3,1). (:1) Find the joint pdf of X and Y and evaluate this pdf at x = y = 0.2. (b) Find the marginal pdf of Y and evaluate this pdf at y = 0.2. (c) Find the marginal mean and variance of Y. (El) Find and sketch the density of R : XY . Then calculate the value of the density at r = 0.25 and illustrate this value in your sketch. (e) Calculate the correlation between X and Y. [10 marks] [10 marks] [10 marks] [20 marks] [10 marks]