In: Statistics and Probability
Do this problem without using any calculus/integration. Suppose that X and Y are jointly continuous random variables with joint density
fX,Y (x, y) = (1/y)exp (−y − (x /y) ), x > 0, y > 0
(a) Find the marginal density of Y and the conditional density of X given Y = y, y > 0
(b) Sketch a plot of the joint pdf
(c) Explain how could you simulate an (X, Y ) pair using an Exponential(1) spinner
(d) Find E(Y ) and Var(Y )
(e) Find E(X|Y ) and Var(X|Y )
(f) Find E(X)
(g) Find Var(X)
(h) Find Cov(X, Y )