I saw this sum in the derivation of the binomial expectation. Anyhow, this is what I have for the probability of having 2 rotten fruits:
prob of having 2 rotten apples * prob of having 0 rotten oranges
+
prob of having 1 rotten apple * prob of having 1 rotten orange
+
prob of having 0...
This is close to the derivation I had, but instead of P(A)^[something] and P(O)^[something], I had two different binomial distributions. I have no problem getting the pdf, but I have trouble simplifying the expectation.
Hi guys,
Here's a description of the problem:
Suppose we have x apples and y oranges where each apple has a probability pa to rot and each orange has a probability po to rot, then what's the pdf of the total number of fruit z being rotten.
This pdf looks like a product of two binomial...