11. The joint moment generating function of two random variables X and Y is defined to be the function M(s, t ) of two real variables defined by M(s, t) = E(esX+tY )

for all values of s and t for which this expectation exists. Show that the jointmoment generating function of a pair of random variables having the standard bivariate normal distribution (6.73)

is M(s, t ) = exp

 1 2 (s2 + 2ρst + t2)



.