# moment generating

• May 15th 2009, 06:50 PM
redpack
moment generating
If the moment generating function of X is $\displaystyle M(t)=\frac{1}{1-3t}$, $\displaystyle t<\frac{1}{3}$
(a) Find E(X)
(b) Find Var(X)
(c) P(6.1<X<6.7)

Thank you!
• May 15th 2009, 08:38 PM
matheagle
X is an EXP rv with parameter $\displaystyle \beta=3$.
Hence the mean and variance is 3 and 9.

Finally part (c) is $\displaystyle {1\over 3}\int_{6.1}^{6.7} e^{-x/3}dx$.
• May 15th 2009, 09:01 PM
redpack
So E(X) is basically the same thing as the mean? Did you just square the parameter / mean to get the variance. For part c, using your equation, I got 0.023727. Thank you for your help.
• May 15th 2009, 09:16 PM
matheagle
Quote:

Originally Posted by redpack
So E(X) is basically the same thing as the mean? Did you just square the parameter / mean to get the variance. For part c, using your equation, I got 0.023727. Thank you for your help.

• May 15th 2009, 11:12 PM
Isomorphism
Quote:

Originally Posted by redpack
Did you just square the parameter / mean to get the variance.

Thats because the distribution in question is exponential... For a general distribution the general method is to write the moment generating function as a power series and identifying the higher order moments.
• May 16th 2009, 03:01 AM
mr fantastic
Quote:

Originally Posted by redpack
If the moment generating function of X is $\displaystyle M(t)=\frac{1}{1-3t}$, $\displaystyle t<\frac{1}{3}$
(a) Find E(X)
(b) Find Var(X)
(c) P(6.1<X<6.7)

Thank you!