The joint continuous distribution of random variables X and Y is given by f X,Y (x,y) = l 2 exp[-lx] for 0 0. = l 2 exp[-lx] * I[ 0

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

f
_X,Y(x,y) = l²exp[-lx]      for        0 < y="">< x="">< ∞ ="" for="" some="" parameter="" l="">0.

               = l²exp[-lx] * I[ 0 < y="">< x="">< ∞="">

******PART B. Identify the marginal distributions of X and Y by type and parameter values.****** (Please help with this part).

Now assume that

l

= 3 to do the numeric computations in parts c and d.

1. 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)).


2. 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:   Comptue E[XY] and then the correlation    r_X,Y
   
   = COV(X,Y)/ [s
   _X
   *s
   _Y
   ].