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 .

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

Al · Accepted Answer

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

PV · Answer

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?