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).
Have no idea where tostart...
Start with the formula: $\displaystyle E(X | Y = y) = \sum_x x \cdot f(x | y)$.
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 $\displaystyle E(X | Y = y) = \sum_x x \cdot f(x | y)$ the summation is the definition of the mean of a Poisson random variable ....