# Moment Generating Function

1. Jan 21, 2010

### zli034

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.

xoxo

2. Jan 22, 2010

Remember that for any random variable

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

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

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

How can you simplify this expression, how does it relate to $$M_X(t)$$,
and how do both observations relate to your problem?

3. Jan 22, 2010

### zli034

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. Jan 22, 2010