moment generating

**redpack** · May 15th 2009, 06:50 PM

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

Thank you!

**matheagle** · May 15th 2009, 08:38 PM

This has been posted already.
X is an EXP rv with parameter $\beta=3$ .
Hence the mean and variance is 3 and 9.

Finally part (c) is ${1\over 3}\int_{6.1}^{6.7} e^{-x/3}dx$ .

**redpack** · May 15th 2009, 09:01 PM

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.

**matheagle** · May 15th 2009, 09:16 PM

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.

mu=mean, just ask MOO

**Isomorphism** · May 15th 2009, 11:12 PM

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.

**mr fantastic** · May 16th 2009, 03:01 AM

Originally Posted by redpack

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

Thank you!

First asked here: http://www.mathhelpforum.com/math-he...-function.html

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