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!

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- May 15th 2009, 06:50 PMredpackmoment 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 PMmatheagle
This has been posted already.

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 PMredpack
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 PMmatheagle
- May 15th 2009, 11:12 PMIsomorphism
- May 16th 2009, 03:01 AMmr fantastic
First asked here: http://www.mathhelpforum.com/math-he...-function.html

Thread closed.