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Math Help - Conditional Expectation question... No idea what to do

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    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).


    Have no idea where tostart...
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    Quote Originally Posted by sebjory View Post
    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: E(X | Y = y) = \sum_x x \cdot f(x | y).
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    thanks very much for your help.

    how ever, i did get to this bit but i found it tough to integrat ethe poisson distribution in this way... i feel im missing something ...
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    Quote Originally Posted by sebjory View Post
    thanks very much for your help.

    how ever, i did get to this bit but i found it tough to integrat ethe poisson distribution in this way... i feel im missing something ...
    It's a sum, not an integral. Please show the work you've done and where you get stuck.
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  5. #5
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    of course the poisson distribution is discrete...

    however this is exactly where im having trouble- what exactly does this summation mean and how do use it?
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    Quote Originally Posted by sebjory View Post
    of course the poisson distribution is discrete...

    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 E(X | Y = y) = \sum_x x \cdot f(x | y) the summation is the definition of the mean of a Poisson random variable ....
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    which is 'y' in this case...

    therefore E(X) is 4p?
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  8. #8
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    Quote Originally Posted by sebjory View Post
    which is 'y' in this case...

    therefore E(X) is 4p?
    It would appear so.
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