The random variables Θ and X are described by a joint PDF which is uniform on the triangular set defined by the constraints 0≤x≤1 , 0≤θ≤x . Find the LMS estimate of Θ given that X=x , for x in the range [0,1] . Express your answer in terms of x using standard notation.

Answer 1

The conditional PDF of Θ given that X=x is uniform on the set [0,x] . Thus, the conditional expectation of Θ given that X=x is equal to x/2 .

Answer 2

Thank you. It was my thoughts too but I wanted to confirm.