- #1

Scootertaj

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**1.Suppose that X~B(1,∏). We sample n times and find n**

a) What is ML estimator of ∏?

b) What is the ML estimator of ∏ given 1/2≤∏≤1?

c) What is the probability ∏ is greater than 1/2?

d) Find the Bayesian estimator of ∏ under quadratic loss with this prior

_{1}ones and n_{2}=n-n_{1}zerosa) What is ML estimator of ∏?

b) What is the ML estimator of ∏ given 1/2≤∏≤1?

c) What is the probability ∏ is greater than 1/2?

d) Find the Bayesian estimator of ∏ under quadratic loss with this prior

**2. The attempt at a solution**

a) [tex]L=\pi^n_1 *(1-\pi)^{n_2}[/tex]

Do [tex]\frac{d(logL)}{d\pi} = \frac{n_1}{\pi} - \frac{n_2}{1-\pi}[/tex] → [tex]\pi_{ML} = \frac{n_1}{n}[/tex]

b) not sure how to go about

c) not sure

d) I think I know how.

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