6. The random variable X is uniformly distributed over the interval [3, 23]. The parameter 3 is unknown and is modeled as the value of a continuous random variable 8, uniformly distributed between zero and one. a Given an observation {13' of X, nd the osterior distribution of 8, 9 X 9 :c . Ex ress P | P your answers in terms of 6' and x. (b) Find the MAP estimate of 8 based on the observation X = a: and assuming that D E a: 5 1. Express your answer in terms of 1:. (c) Find the LMS estimate of 8 based on the observation X = a: and assuming that D g :1: g 1. Express your answer in terms of x. {(1) Find the linear LMS estimate dLLMS of 8 based on the observation X = x