4. (10 points) Suppose f (x0) is the uniform density over the interval 0≤x≤0. Assuming that has a prior density of (0) =

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4 10 Points Suppose F X0 Is The Uniform Density Over The Interval 0 X 0 Assuming That Has A Prior Density Of 0 1 (11.19 KiB) Viewed 78 times

Suppose f(x|theta) is the uniform density over theinterval 0<=x<=theta.
Assuming that theta has a prior density of pi(theta) =B^2*theta*exp[-B*theta] for theta >0:
a) What is the posterior density f(theta|x)?
b) Compute the MMSE estimate for theta.
4. (10 points) Suppose f (x0) is the uniform density over the interval 0≤x≤0. Assuming that has a prior density of (0) = ß²0 exp(-BO) for 0 > 0: a) What is the posterior density f (0 | x)? b) Compute the MMSE estimate for 8.