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Flip 100 Coins
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.
Solution
is the amount of heads. E[X] is equal to 
. The expected value of the number of interest is given by (1) 
is already known, which is 50. 
has to be estimated as follows. (2) 
is given by the binomial distribution. For 
and 
, we have (3) 
(4) 
(5) 
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