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lordy12
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1. http://d.imagehost.org/t/0866/problem1.jpg
3. For the Poisson random variables I get ((lamda)^x)/((e^2lambda)*x!) when y =1. Is this a Poisson Random variable? Also, when y = 0, I get ((lamda)^x)/((e^lambda)*x!) - ((lamda)^x)/((e^2lambda)*x!) I cannot get the binomial. I don't know how to show that this is Binomial as x is in the range from 1...infinity.
For part 1 I used the fact that P(X=x and Y=y) = P(X|Y)P(Y)
and P(Y=y) = sum(1 to x)P(X=x and Y=y) = 1, so P(X=x|Y=y)(P(y) = P(X=x and Y=y)
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Homework Equations
3. For the Poisson random variables I get ((lamda)^x)/((e^2lambda)*x!) when y =1. Is this a Poisson Random variable? Also, when y = 0, I get ((lamda)^x)/((e^lambda)*x!) - ((lamda)^x)/((e^2lambda)*x!) I cannot get the binomial. I don't know how to show that this is Binomial as x is in the range from 1...infinity.
For part 1 I used the fact that P(X=x and Y=y) = P(X|Y)P(Y)
and P(Y=y) = sum(1 to x)P(X=x and Y=y) = 1, so P(X=x|Y=y)(P(y) = P(X=x and Y=y)
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