15.1 . Let W = ln Y − ln 100 = ln(Y/100). Then y = 100ew and dy = 100ewdw. Thus,
which is a Pareto density with α = 12 and θ = 4.801121.
which is a gamma distribution with parameters 10 + γ and . The mean is . For the mle:
for . The two estimators are equal when γ = 0 and θ = ∞, which corresponds to π(α) = α−1, an improper prior.
and the solution is . Also,
and so .
which is a normal pdf with mean and variance ...