probability from moment generating function?

#1
if the moment generating of a random variable X is

M_x(t)=(1-t)^-2

compute P(-2 < X < 3) or explain why it cannot be computed

how do I do this? I tried calculating EX and EX^2 and got 2 and 6 but i have no idea how to proceed...
 

Martingale

TS Contributor
#2
if the moment generating of a random variable X is

M_x(t)=(1-t)^-2

compute P(-2 < X < 3) or explain why it cannot be computed

how do I do this? I tried calculating EX and EX^2 and got 2 and 6 but i have no idea how to proceed...
the MGF here is from a well known distribution
 
#3
ah! ok i got it i think! it;s a gamma distri!

then i have to integrate x e^-x dx... which is the pdf... i wiki-ed integration (i've forgotten most of mine.. havent used it in a while...) and found a formula and applied it directly and got an answer, but i was wondering, to integrate that, is the method called integration by parts?

thank you so much!! :D
 

Martingale

TS Contributor
#4
ah! ok i got it i think! it;s a gamma distri!

then i have to integrate x e^-x dx... which is the pdf... i wiki-ed integration (i've forgotten most of mine.. havent used it in a while...) and found a formula and applied it directly and got an answer, but i was wondering, to integrate that, is the method called integration by parts?

thank you so much!! :D
yes it is a gamma dist and yes you have to use integration by parts