1. ## Expected Value - Help PLEASE!!!

How do you find E(1/X)? X is distributed binomially with probability p and n+1 terms: X~Binom(n+1, p). So E(X) = p(n+1), but how do I find E(1/X)?
Any help is much appreciated, thank you!

2. ## Re: Expected Value - Help PLEASE!!!

This is what I think I need to know for the problem anyway. For anyone who's interested, the whole problem is: Alice and her n friends (a total of n+1 people) decide the following rule for sharing a cash prize totaling K dollars. The K dollars will be divided by the number of people who get a head tossing a p-coin. What is expected prize for Alice?

3. ## Re: Expected Value - Help PLEASE!!!

A question: What if all of you get a tail? In terms your first post it means that which makes the expectation infinite.

4. ## Re: Expected Value - Help PLEASE!!!

If everyone gets a tail, no one gets any prize money, so that part of the expected value goes to zero

5. ## Re: Expected Value - Help PLEASE!!!

Now the formulation is clear.
Let be the number of heads obtained by her friends.
Conditional on she obtain a head or not, the expected value is

6. ## Re: Expected Value - Help PLEASE!!!

Thank you, but I still don't quite understand. K is constant, so you can pull that out, but then I am still left with the problem of E(1/(1+x)), which is similar to what I asked initially of how to solve E(1/X). My answer should be in terms of n,p, and K.

When I initially tried to solve this problem, I set X~Binom(n+1, p) to be the number of heads obtained by her and her friends, found the expected value of that, and divided K by E(X). However, that is K(1/E(X)), and I think the answer should be K(E(1/X)). Can I say these two values are equal? I'm not sure...

7. ## Re: Expected Value - Help PLEASE!!!

The expected value can be calculated directly by definition:

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