Question

finding means, variances and correlation coefficient of X and Y of p(x,y)=e^-2/[x!(y-x)!] , y=0,1,2...
x=0,1,...y

Answer 1

i have found the mgf of this joint distribution it is
\[e ^{-2}e ^{e _{}^{t}(e ^{s}+1)}\]

Answer 2

you found the hardest part of this problem...where are you stuck?

Answer 3

to find the mean take derivative but with respect to what? and set to 0

Answer 4

\[M_{X,Y}(s,t)=E\left[e^{sX+tY}\right]\]

\[\frac{d}{dt}E\left[e^{sX+tY}\right]=E\left[Xe^{sX+tY}\right]\]

set s,t =0

\[=E\left[Xe^{0X+0Y}\right]=E[X]\]