What is moment generating function?
1 Answer
Answer:
See below.
Explanation:
The parameters

The
#k# th moment of a random variable#Y# taken about the origin is defined to be#E(Y^k)# and is denoted by#mu_k^'# 
The momentgenerating function
#m(t)# for a random variable#Y# is defined to be#m(t)=E(e^(tY))# . We say that a momentgenerating function for#Y# exists if there exists a positive constant#b# such that#m(t)# is finite for#abs(t) <= b#
If
#(d^km(t))/(dt^k)]_(t=0)=m^(k)(0)=mu_k^'#
In other words, if you find the
Then we find that various probability distributions have their own unique momentgenerating function.