If X and Y have a bivariate normal distribution, it can be shown that their joint moment€“ generating function (see Exercise 4.48 on page 139) is given by

Verify that
(a) The first partial derivative of this function with respect to t1 at t1 = 0 and t2 = 0 is µ1;
(b) The second partial derivative with respect to t1 at t1= 0 and t2 = 0 is σ21 + µ21;
(c) The second partial derivative with respect to t1 and t2 at t1 = 0 and t2 = 0 is ρσ1σ2 + µ1µ2.

Transcribed Image Text:

eti μι +12 μ 2十t@ft[+ 2pơio211t2 tost_ )