We are given a biased coin, where the probability of Heads is q. The bias q...

 
 

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We are given a biased coin, where the probability of Heads is q. The bias q is itself the realization of a random variable which is uniformly distributed on the interval [0, 1]. We want to estimate the bias of this coin. We flip it 5 times, and define the (observed) random variable N as the number of Heads in this experiment. Throughout this problem, you may find the following formula useful: For every positive integers n, k, 1 S² =² x" (1 − x) dx = For 0 ≤ q ≤ 1, fQN (9| N = 3) = n!k! (n + k + 1)!* 1. Given the observation N = 3, calculate the posterior distribution of the bias Q. That is, find the conditional distribution of Q, given N = 3. 2. What is the LMS estimate of Q, given N 3? QLMS 3. What is the resulting conditional mean squared error of the LMS estimator, given N = 3? We are given a biased coin, where the probability of Heads is q. The bias q is itself the realization of a random variable which is uniformly distributed on the interval [0, 1]. We want to estimate the bias of this coin. We flip it 5 times, and define the (observed) random variable N as the number of Heads in this experiment. Throughout this problem, you may find the following formula useful: For every positive integers n, k, 1 S² =² x" (1 − x) dx = For 0 ≤ q ≤ 1, fQN (9| N = 3) = n!k! (n + k + 1)!* 1. Given the observation N = 3, calculate the posterior distribution of the bias Q. That is, find the conditional distribution of Q, given N = 3. 2. What is the LMS estimate of Q, given N 3? QLMS 3. What is the resulting conditional mean squared error of the LMS estimator, given N = 3?

Answer rating: 100% (QA)

Answer Solution Hele N heads out of 5 toss where plHead ... View the full answer