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The random variable X is uniformly distributed over the interval [9, 29]. The parameter 6 is unknown and is modeled as the value of a continuous random variable 8, uniformly distributed between zero and one. 1. Given an observation cc of X, find the posterior distribution of 8. Express your answers below in terms of 3 and cc. Use 'theta" to denote 6 and 'ln" to denote the natural logarithm function. For example, In (9) should be entered as 'ln(theta)'. ForOmSlandx/Zggm: 0 2. Find the MAP estimate of 8 based on the observation X : a: and assuming that 0 S a: S 1. Express your answer in terms of (r. ForOSmSl: [l 3. Find the LMS estimate of 9 based on the observation X = a: and assuming that 0 S at S 1. Express your answer in terms of at. ForOSmSl: 0 4. Find the linear LMS estimate LLMS of 8 based on the observation X = 3:. Specifically, LLMS is of the form 61 + c233. Find (:1 and c2. 3' _x c1 C2