43. The bivariate random variable (P,Q) represents the weekly price, in dollars, and the quantity, in number of kegs, of an India Pale Ale beer, HopMeister, sold in the Pacific Northwest market. The moment generating function associated with this bivariate random variable is given by Mð Þ P;Q ðtÞ ¼ exp m0 t þ :5t0 ð Þ
t , where m ¼ 125 500   and
¼ 100 100 100 400  :

(a) What is the expected weekly price of HopMeister?

(b) What is the expected weekly quantity sold of HopMeister?

(c) What is the expected weekly dollar sales of HopMeister?