Question: 2. Let X1, . . . , Xn be a random sample from Uniform[0, ] where > 0 is unknown. (a) Show that b =

2. Let X1, . . . , Xn be a random sample from Uniform[0, ] where > 0 is unknown.

(a) Show that b = max{X1, . . . , Xn} is the MLE of .

(b) Let the CDF of b be F(). Find F(t) for any t R.

(c) Find the pdf of b.

(d) What is the distribution of / b ? Give the distribution name and parameter values.

(e) How large a random sample must be taken in order thatPr(|b | 0.1) 0.95 for all possible ?

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