As in Problem 7 6 3, let X1, , Xn be a set of independent random variables with a U (0, ) distribution, and let T max X1, , Xn) Explain why the likelihood function L(x1, , xn, ) is equal to 1 n if t max x1, , xn), and is equal to 0 otherwise Sketch the likelihood function against , and deduce that ...

Recall that fx i 1 for 0 x i an ...

As in Problem 7.6.3, let X1,..., Xn be a set of independent random variables with a U

Question:

As in Problem 7.6.3, let X1,..., Xn be a set of independent random variables with a U (0, θ) distribution, and let
T = max{X1,..., Xn)
Explain why the likelihood function L(x1,..., xn, θ) is equal to
1/θn
if θ ≥ t = max{x1,..., xn), and is equal to 0 otherwise. Sketch the likelihood function against θ, and deduce that the maximum likelihood estimate of θ is θ = t. What is the bias of this point estimate?