For a certain coin q is a uniform 0 1 random variable, Basic Statistics

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For a certain coin q is a uniform 0 1 random variable

For a certain coin, Q, is a uniform (0, 1) random variable. Given Q = q, each flip is heads with probability q, independent of any other flip. Suppose this coin is flipped n times. Let K denote the number of heads in n flips.

(a) What is the ML estimator of Q given K?

(b) What is the PMF of K? What is E[K]?

(d) Find the MMSE estimator of Q given K = k.

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Basic Statistics: For a certain coin q is a uniform 0 1 random variable

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