You can use Wald's Equation directly or copy the proof for your case...
Wald's equation - Wikipedia, the free encyclopedia
(Hint: Use proof 2)
But Wald says that .
I need to solve this problem using conditional expectation:
A hen lays N eggs where N is Poisson with parameter k. The weight of the nth egg is Wn where W1, W2, ... are independent identically distributed random variables with mean x. Let W=sum from i=1 to i=N of Wi.
Show E[W]=xk
Any help would be hugely grateful!
p.s. sorry for my poor inputting, im a newbie!
You can use Wald's Equation directly or copy the proof for your case...
Wald's equation - Wikipedia, the free encyclopedia
(Hint: Use proof 2)
But Wald says that .
It seems that if N is also independent, you don't need Wald's equation, just the simple rules of conditional expectation are enough.... (see Compound Poisson process - Wikipedia, the free encyclopedia and Law of total expectation - Wikipedia, the free encyclopedia)
I'm trying to figure out where the independence of N is needed in this elementary proof, but so far I haven't been able. But it must be needed, otherwise Wald's equation wouldn't have the quite complex proof it has.
Someone can help me?