Asked by Anonymous
We are given a biased coin, where the probability of Heads is q. The bias q is itself the realization of a random variable Q 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.
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.
For 0≤q≤1,
2) What is the LMS estimate of Q, given N=3?
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.
For 0≤q≤1,
2) What is the LMS estimate of Q, given N=3?
Answers
Answer
1.140*y^3*(1-y)^3
2.0.5
3. What is the resulting conditional mean squared error of the LMS estimator, given N=3?
ans. 1/36
2.0.5
3. What is the resulting conditional mean squared error of the LMS estimator, given N=3?
ans. 1/36
Answered by
roger
any hint, how did you do the calculation?
Answer
This is the case for flipping 6 times.
Answered by
Mac
Hint: Use a normalization constant for the Bayes theorem
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