You flip a coin 100 times. Let X= the number of heads in 100 flips. Assume...
You flip a coin 100 times. Let X= the number of heads in 100 flips. Assume we don’t know the probability, p, the coin lands on heads (we don’t know its a fair coin). So, let Y be distributed uniformly on the interval [0,1]. Assume the value of Y = the probability that the coin lands on heads.
So, we are given Y is uniformly distributed on [0,1] and X given Y=p is binomially distributed on (100,p).
Find E(X) and Var(X).
Hint: Will use either 1. Law of Total Expectation: E(X) = E[E(X|Y)] or 2. Law of Total Variance: Var(X) = E[Var(X|Y)] + Var[E(X|Y)]
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