# Homework Help: Moment generating function problem

1. Aug 16, 2011

### wannabe92

From the pdf of X, f(x) = 1/8 e^-x/8, x > 0, find the mgf of Y=X/4 +1. What is then the value of P(2.3 < Y < 4.1)?
1. The problem statement, all variables and given/known data

2. Relevant equations
Moment generating function of exponential distribution

3. The attempt at a solution
I have the mgf of X, which is 1/8 / (1/8 - t). I have also worked out the mgf of Y, which is e^t (1/8 (1/8 - t/4)), I think. The last part of this problem I've yet to resolve. Please do help!

Last edited: Aug 16, 2011
2. Aug 17, 2011

### Ray Vickson

Please state exactly what definition of mgf you are using; the one that I use (standard, I think) gives a very different result from yours.

As to the second question: I don't think the mgf has any relevance here; you need to relate the interval probabilities of Y to those of X, and use the density of X to compute the result. In other words, {a <= Y <= b} is the same as {a1 <= X <= b1} for some a1 and b1 related to a and b, and you know how to calculate P{a1 <= X <= b1}.

RGV

3. Aug 17, 2011

### wannabe92

I'm using the mgf of exponential: lambda/(lambda -t). So, to obtain the probability, simply integrate the probability density function of X with the values of a1 and b1, is that it?