SOLUTION: I have a homework question that has me stumped. Desperatedly need help.
A random variable X has moment generating function M(t) = (1-t)^-1. Find the rth moment of X.
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Question 349587: I have a homework question that has me stumped. Desperatedly need help.
A random variable X has moment generating function M(t) = (1-t)^-1. Find the rth moment of X.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Look at the derivatives of evaluated when .
The rth moment is the rth derivative of evaluated at .
1st derivative:
.
.
2nd derivative:
3rd derivative:
4th derivative:
5th derivative:
.
.
.
Hopefully you see the pattern here,
.
.
.
1st derivative:
2nd derivative:
3rd derivative:
4th derivative:
5th derivative:
.
.
.
rth derivative: *...*=
.
.
.
So the rth moment of is .
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