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Question: i we are interested in testing for fairness of a...

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I. We are interested in testing for fairness of a coin. Let θ e (0,1) denote the probability of the coin landing on heads, and consider testing Ho : θ = 0.5 versusHı : θ > 0.5. We toss the coin until we see the first head. Let X denote the number of tosses. (a) (10 points) Show that the uniformly most powerful test rejects Ho if X c, where c > 1 is some constant to be determined.

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