(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X and Y are joointly distributed discrete random variables with probability mass function

p_{X,Y}(x,y)=(c/e^{c})(1-c)^{x}c^{y}/y!, x,y=0,1,2,..., 0<c<1

Find E(X^{Y})

2. Relevant equations

3. The attempt at a solution

How can we calculate this double sum? We can pull out the constant c/eCode (Text):By definition,

E(X[SUP]Y[/SUP])

∞ ∞

= ∑ ∑ x[SUP]y[/SUP] (c/e[SUP]c[/SUP])(1-c)[SUP]x[/SUP]c[SUP]y[/SUP]/y!

x=0 y=0

^{c}, but what's next?

Thanks for any help!

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# Homework Help: Expected Value: E(X^Y)

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