Thread: 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?

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



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



I hope that helps.

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.

Use the derivatives, and it will work.

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

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

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.