Suppose that a random sample of four observations is to be drawn from the uniform distribution on the interval [0, ], and that the prior

Suppose that a random sample of four observations is to be drawn from the uniform distribution on the interval [0, θ], and that the prior distribution of θ has the following p.d.f.:

Suppose that the values of the observations in the sample are found to be 0.6, 0.4, 0.8, and 0.9. Determine the Bayes estimate of θ with respect to the squared error loss function.

for > otherwise. 0