2-D has a biased coin for the which the probability of getting tails is an unknown...

  

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2-D has a biased coin for the which the probability of getting tails is an unknown p. He decide to flip the coin 200 and get tails a total of 146. Find the 95% confidence interval for the true success probability p. Let the joint p.m.f. of (X,Y) be PX,Y (k, n) = n+1 0 else. n+1 *-1-1 for 1 <n<∞0 and 1 ≤k<∞, 1. Find the p.m.f. py (n) of X and the conditional p.m.f pxy (kin). Calculate E[Y]. 2. Find the conditional expectation E[X|Y]. 3. Use parts 1. and 2. to calculate E[X]. 2-D has a biased coin for the which the probability of getting tails is an unknown p. He decide to flip the coin 200 and get tails a total of 146. Find the 95% confidence interval for the true success probability p. Let the joint p.m.f. of (X,Y) be PX,Y (k, n) = n+1 0 else. n+1 *-1-1 for 1 <n<∞0 and 1 ≤k<∞, 1. Find the p.m.f. py (n) of X and the conditional p.m.f pxy (kin). Calculate E[Y]. 2. Find the conditional expectation E[X|Y]. 3. Use parts 1. and 2. to calculate E[X].