Let X1, X2, and X3 be random variables, either continuous or discrete. The joint
Chapter 5, Problem 5.164(choose chapter or problem)
Let X1, X2, and X3 be random variables, either continuous or discrete. The joint momentgenerating function of X1, X2, and X3 is defined by m(t1, t2, t3) = E(et1 X1+t2 X2+t3 X3 ). a Show that m(t, t, t) gives the moment-generating function of X1 + X2 + X3. b Show that m(t, t, 0) gives the moment-generating function of X1 + X2. c Show that k1+k2+k3m(t1, t2, t3) t k1 1 t k2 2 t k3 3 t1=t2=t3=0 = E Xk1 1 Xk2 2 Xk3 3 .
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