Let X1,..., Xn be a set of independent random variables with a U(0, θ) distribution, and let
T = max{X1,..., Xn}
(a) Explain why the cumulative distribution function of T is
F(t) = (t/θ)n
For 0 ‰¤ t ‰¤ θ.
(b) Show that the probability density function of T is

for 0 ‰¤ t ‰¤ θ.
(c) Show that

is an unbiased point estimate of θ.
(d) What is the standard error of ?
(e) Suppose that n = 10 and that the following data values are obtained:

What are the values of θ and the standard error of θ?

Transcribed Image Text:

1R-1 f(t) = n n+ 1 1 1.2 6.3 7.3 6.4 3.5 0.2 4.6 7.1 5.0 1.8