土豆泥
the definition of mgf:M(t)=E(e^tx)
if X1 and X2 are independent, then M(t1,t2)=E(e^t1x1+e^t2x2)
为何是 e^t1x1和e^t2x2相加的expectation呢？对mgf不适很理解，所以出现这种joint
mgf就更搞不
清楚了。谢谢
lovetan
Since the mgf of X (random variable) is
M(X)(t)=E(e^tX)=∫(e^tX)f(x)dx
Then , the joint mgf of X1 and X2 is
M(X1,X2)(t1,t2)=E(e^(t1*X1+t2*X2))=∫[e^(t1*X1+t2*X2)]f(x1,x2)dx1dx2
And if the X1 and X2 are independent, then
M(X1,X2)(t1,t2)=M(X1)(t1)*M(X2)(t2)
