Conditional Expectation question... No idea what to do
Let Y Bin(4; p) and assume that the conditional distribution of X given that Y = y is
Poi(y). Write down E(X/Y = y). Use the formula E(X) = E(E(X/Y )) to nd E(X).
Let Y Bin(4; p) and assume that the conditional distribution of X given that Y = y is
Poi(y). Write down E(X/Y = y). Use the formula E(X) = E(E(X/Y )) to nd E(X).
however this is exactly where im having trouble- what exactly does this summation mean and how do use it?
You're meant to recognise that when you substitute the conditional pdf into the summation is the definition of the mean of a Poisson random variable ....