Random variableXis uniformly distributed over the interval [,2]. The parameteris unknown and is modeled as the value of a continuous random variable , uniformly distributed between zero and one.

(a)Given an observationx[0,1] ofX, find the posterior distribution of ,f|X(|x). Express your answers in terms ofandx.

(b)Find the MAP estimate of givenX=x, assuming that 0x1. Express your answer in terms ofx.

(c)Find the LMS estimate of givenX=x, assuming that 0x1. Express your answer in terms ofx.