Moment-Generating Functions for Z = 1/4(X-3)

[alexdude777]

Homework Statement

Given moment-generation function Msubx(t) = e^(3t+8t^2) find the moment-generating function of the random variable Z = 1/4(X-3) and use it to determine the mean and the variance of Z

Homework Equations

The Attempt at a Solution

Honetly I have no idea where to begin. This is the only question I can find of this format in my book that is worded like this, and the examples in my stats book leading up to this just don't cover a question like this, it's all theorems and more basic questions. I messed up my tailbone VERY badly last week and had to miss 2 of my stats lectures which has put me in this position.

Can someone just help get me started on this and know what I need to do?

The only thing I can think of is that I have to multiply the Msubx(t) function by e^(tx) and somehow relate it to the r.v. Z?

I am so confused...not asking for someone to do this for me but could you at least get me started??

Thanks so much.

 

[korican04]

Msubx(t) = e^(3t+8t^2) is the moment generation function for a normal distribution.

The moment-generating function of N(mean,sigma_squared) is
Msubx(t)= e^(mean*t+.5*sigma_squared*t^2),

so in this case the mean is 3 and sigma_squared = 16,
Now try finding the mu and sigma for Z based on the stats for X and then you can use them to write out the moment generation function.

Is Z=1/(4*(X-3)) or Z=.25*(X-3)? just curious.