Fall 2011 Strategic Practice 10: Section 1 (Conditional Expectation and Conditional Variance) - Question 5
One of two identical-looking coins is picked from a hat randomly, where one coin has probability of Heads and the other has probability of Heads. Let X be the number of Heads after flipping the chosen coin n times. Find the mean and variance of X.
The distribution of X is a mixture of two Binomials; we have seen before that X is not Binomial unless p1 = p2. Let I be the indicator of having the p1 coin. Apply Adam's Law and Eve's Law.
Consult iTunes course for full solution.
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