If the moment generating function of X is ,

A. Find E(X)

B. Find Var(X)

C. P(6.1 < x < 6.7)

Thank you in advance for your help!

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- May 3rd 2009, 01:47 PMlogitechmoment generating function
If the moment generating function of X is ,

A. Find E(X)

B. Find Var(X)

C. P(6.1 < x < 6.7)

Thank you in advance for your help! - May 3rd 2009, 02:10 PMMoo
Hello,

By definition, , where denotes the n-th derivative of the mgf.

Specifically, and

For Var(X), recall the formula I put before : E(X²)-[E(X)]²

For question C., I don't know... Your mgf is the mgf of an exponential distribution with parameter 1/3, which would finish the question, by using the cumulative distribution function.

I'm looking for a way without "recognizing" the mgf, but it looks like there isn't any. - May 3rd 2009, 02:28 PMlogitech
This one is still difficult for me to understand. Thank you for trying to help me understand this one. I will keep working on it. I wish you could be my tutor! Taking an online class basically means there is no teacher, just a textbook and a list of work to do.

- May 3rd 2009, 02:46 PMmatheagle
MGF's are unique

This is a gamma with and

Hence the mean is

and the variance is

and yes, ms mathbeagle, now you can integrate the density to obtain the probabilities. - May 16th 2009, 03:02 AMmr fantastic
See this thread also: http://www.mathhelpforum.com/math-he...enerating.html