MSE(YLMS|N=3)=?
Answer:
fY|N(y∣N=3)=6y^3(1-y)^3
YLMS=0.5
MSE(YLMS|N=3)=0.125
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 ,
∫10xn(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)=?
What is the LMS estimate of Y , given N=3 ?
(Enter enter image description herean exact expression or a decimal accurate to at least 2 decimal places.)
YLMS=?
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.)
1 answer