Question

Helpppppp pls!

The probability of Heads of a coin is y, and this bias y is itself the realization of a random variable Y which is uniformly distributed on the interval [0,1].

To estimate the bias of this coin. We flip it 6 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,
∫1,0 x^n(1−x)^kdx=n!k!(n+k+1)!.


Given the observation N=3, calculate the posterior distribution of the bias Y. That is, find the conditional distribution of Y, given N=3.

For 0≤y≤1,

fY|N(y∣N=3)=
unanswered

What is the LMS estimate of Y, given N=3?

(Enter an exact expression or a decimal accurate to at least 2 decimal places.)

Y^LMS= unanswered

What is the resulting conditional mean squared error of the LMS estimator, given N=3?

(Enter an exact expression or a decimal accurate to at least 2 decimal places.)

unanswered

Answer 1

This is my solution.

1) fY|N(y∣N=3)=84 y^6 (1-y)^3
2)0.0636363
3)0.0383746

it's correct?