Flip 100 coins

Expected Value
If I flip 100 coins and then multiply the number of heads by the number of tails, what is the expected value of that number?

Hint

It's not 50 * 50. Think about the variance.

Answer

is the amount of heads. E[X] is equal to . The expected value of the number of interest is given by

(1)  

Here, is already known, which is 50. has to be estimated as follows.

(2)  

The variance of is given by the binomial distribution. For and , we have

(3)  

So, now we know that

(4)  

Then we can conclude that

(5)