Moment Generating Function

  • Thread starter zli034
  • Start date
  • #1
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Main Question or Discussion Point

Say r.v. X, we have pdf f(x) and mgf Mx(t) defined.

Then define Y=-X, y is negative x.

Can we get mgf of Y, i.e. My(t) and how?

I know I can go the way to get pdf f(y) first then My(t). I want to know if Mx(t) is already in my hands, it should be easier to get My(t) other than do f(y) first.

I thought about this whole afternoon. Just don't get it. Please help and thanks in advance.

xoxo
 

Answers and Replies

  • #2
statdad
Homework Helper
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Remember that for any random variable

[tex]
M_x(t) = E[e^{tx}]
[/tex]

If you want the mgf for cX (any constant times X)

[tex]
M_{cX}(t) = E[e^{t(cx)}]
[/tex]

How can you simplify this expression, how does it relate to [tex] M_X(t)[/tex],
and how do both observations relate to your problem?
 
  • #3
107
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I have found one way.

I have here x=log(1-x) and f(x) also known.

So we can see if I put x=log(1-x) in to Mcx(t), it can be simplified easily. Here is my solution for this problem and it depends on the form of function of x.
 
  • #4
statdad
Homework Helper
1,495
35
How does your second post relate to your first question?
 

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