# Thread: MGF moment help?

1. ## MGF moment help?

If X has the moment generating function
M(t) = (e^ ((PI)*t ) - e^ (et) ) / t
find E (X), V ar (X), and P (2.8 <= X < 3). help please?

2. What you need to do get E[X] is to evaluate the first derivative of M(t) at t=0.

$E[X]=\frac{d}{dt}M(0)$

For the variance, you need to find the second derivative of M(t) and E[X].

$Var(X)=E[X^2]-(E[X])^2=\frac{d^2}{dt^2}M(0)-(E[X])^2$

I hope that helps.

3. I don't think that function works or is correct. I think my professor made a mistake because the limit as t approaches 0 of M(t) is π - e, but this limit should always be 1.

4. Use the derivatives, and it will work.

5. I know this will sound like the dumbest question ever, but I'm never sure when to apply derivatives or integrals!

6. i got what i got before
1.24
http://www.wolframalpha.com/input/?i=(-e^2+%2B+pi^2)/2
the limit of the derivative of the mgf
as t approaches 0 is that function
and that function is not 1
oh wait, but thats allegedly the mean
i dunno, i don't think its a pdf

7. Originally Posted by Intsecxtanx
I don't think that function works or is correct. I think my professor made a mistake because the limit as t approaches 0 of M(t) is π - e, but this limit should always be 1.
You're correct. The given function is not a valid mgf, for the very reason you state.

Originally Posted by akolman
Use the derivatives, and it will work.
Since the given function is not a valid mgf there is no point doing this.