Question

Let X and Y be jointly continuous nonnegative random variables. A particular value y of Y is observed and it turns out that fX|Y(x∣y)=2e−2x , for x≥0 .

Find the LMS estimate (conditional expectation) of X .
unanswered

Find the conditional mean squared error E[(X−XˆLMS)2∣Y=y] .
unanswered

Find the MAP estimate of X .
unanswered

Find the conditional mean squared error E[(X−XˆMAP)2∣Y=y] .
unanswered

Answer 1

a) 1/2
b) 1/4
c) 0
d) 1/2

Answer 2

Can you show your calculations for a)?

I got a different result: 1/4

E[X|Y=y] = integral x*fX|Y(x|y)dx
= integral(infinity to 0) x*2e^(-2x) dx
=1/4

Am i wrong here?