Moment generating distribution doubt

[Homer Simpson]

Q) If two random variables have joint Density function -

f(x,y)  = e^(-x-y)    for x>0, y>0
         = 0               elsewhere

Find their joint moment generating function and use it to determine E(XY).

How to do this??

[kangkan]

Mx(t)=E(e^tx)= double int from 0 to infinity e^tx. e^-x. e^-y..

solving we get Mx(t)=1/1-t =1+t+t^2+t^3= 1 +1!*t/1! +2!*t^2/!.......therefore u=1!=1

i hope this is right :)

[Homer Simpson]

Thank you, I understood how to find the moment generating function but didnt get the part about E(XY)

[kangkan]

Hi...do you have freund ?..i can refer to page number

[Homer Simpson]

yeah please do so :) i have the 8th edition

[kangkan]

oops i have 7th...but its in chapter 4..my page number 144....example 4.13 the question is f(x)=E^-x....derive the mgf and moments....at the end of this question,they explain the concept

[Homer Simpson]

acha, i will check again. still not super clear on moments anyway! thank you :)