Can someone explain to me how this problem works?

Given the moment generating function Mx(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.

I don't understand why its asking you to find another mgf if one is given to you already. Thanks!

See 6.7 here: http://www.am.qub.ac.uk/users/g.gribakin/sor/Chap6.pdf

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  

Mx(t)=e^(3t+8t^2) is the MGF of X

you are asked to get the MGF of Z=X/4-3/4 if I understand your ().

Hm, so I read through what was posted and my textbook, but I still don't quite understand. So I have the MGF of X, then to get the MGF of Z do I need to integrate Z from negative to positive infinity and somehow subsitute in X? This is really confusing me, any help is appreciated thanks!

Just substitute, or recognize the distribution of X and use that.

Z=X/4-3/4

So



Plug in t/4 for t in the mgf of X and examine what you have.

You're probably expected to know and apply the result found at the bottom of page 1 here: http://web.as.uky.edu/statistics/use...320u04/mgf.pdf

In fact, it's the same result that I refered you to in my first reply. Did you in fact bother to click on the link and look at it?

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  

Hi, I've been working on the same problem and came to the answer
Mz(t)=e^[(4/5)t^2]

Is this the answer that you came to?

I get a different answer. Please pm me your working.

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  

Oopsie!! I just went over my calculation and realized I made a mistake. My new answer is

Mz(t)=e^[(1/2)t^2]

Is that correct?

Yes.

__________________
There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  
• 
  To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.
  

The point of this problem is that a linear transformation of a normal is a normal.
The mean and variance should be easy to calculate directly.