The joint continuous distribution of random variables X and Y is given by

f _X,Y(x,y) = l²exp[-lx] for0 0.

= l²exp[-lx] * I[ 0

a.Are X and Y independent? Explain.

b.Identify the marginal distributions of X and Y by parameter values and type.

Now assume that l = 3 to do the numeric computations in parts c and d.

c.Using your findings in part b. you can simply state the means E[X] and E[Y] and variances VAR[X]and VAR[Y]. (to be used below in CORR(X,Y)).

d.Using part b, Can you state the conditional expectation E[Y | X =x] for all possible values x of X?

Using part d if possible or else directly from your joint probability table:Compute E[XY] and then the correlationr_X,Y = COV(X,Y)/ [s_X*s_Y].

PROBLEM 2. The joint continuous distribution of random variables X and Y is given by fxwxy) = >exp[-Ax] for 0 for some parameter > >0. - Nexp[-Ax] * 10