Suppose that the number of minutes a person must wait for a bus each morning has the uniform distribution on the interval [0, θ], where the value of the endpoint θ is unknown. suppose also that the prior p. d.f. of θ is as follows: ξ(θ ) = 192 θ 4 for θ ≥ 4, 0 otherwise.

if the observed waiting times on three successive mornings are 5, 3, and 8 minutes, what is the posterior p. d.f. of θ?