Conditional Expectation question... No idea what to do

• Jan 21st 2009, 12:05 PM
sebjory
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...
• Jan 22nd 2009, 01:00 PM
mr fantastic
Quote:

Originally Posted by sebjory
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: $\displaystyle E(X | Y = y) = \sum_x x \cdot f(x | y)$.
• Jan 22nd 2009, 02:54 PM
sebjory
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 ...
• Jan 22nd 2009, 05:56 PM
mr fantastic
Quote:

Originally Posted by sebjory
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.
• Jan 23rd 2009, 02:36 AM
sebjory
of course the poisson distribution is discrete...(Rofl)

however this is exactly where im having trouble- what exactly does this summation mean and how do use it?
• Jan 23rd 2009, 04:17 AM
mr fantastic
Quote:

Originally Posted by sebjory
of course the poisson distribution is discrete...(Rofl)

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 ....
• Jan 23rd 2009, 03:01 PM
sebjory
which is 'y' in this case...

therefore E(X) is 4p?
• Jan 24th 2009, 02:03 AM
mr fantastic
Quote:

Originally Posted by sebjory
which is 'y' in this case...

therefore E(X) is 4p?

It would appear so.