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 micro 1 (b) The second partial derivative with respect to t1 at t1 0 and t2 0 is Iuml 21 micro 21 (c) The second partial derivative with respect to t1 and t2 at t1 0 and t2 0 is Iuml Iuml 1 Iuml 2 micro 1 micro 2 eti 12 2t ft 2pio211t2 tost )

Question: 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)

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 Ïƒ21 + µ21;
(c) The second partial derivative with respect to t1 and t2 at t1 = 0 and t2 = 0 is ÏÏƒ1Ïƒ2 + µ1µ2.

eti +12 2t@ft[+ 2pio211t2 tost_ )

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