d) Suppose that X,,X2, .,X, is a random sample from a distribution with probability density function: x-01 if x 2 0, and – o < 02 < ∞ f(x; 0,02) = {0, 0, else where If 0, = 0, i) show whether or not E, X, is a minimal sufficient statistic for 02. i) Show whether or not E1 Xt is a pivotal quantity. Give two reasons why or why not it is a pivotal quantity. ii) What is the distribution of E, X1.

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d) Suppose that X,,X2, ., X, is a random sample from a distribution with
probability density function:
x-01
if x 2 0, and – 0o < ®2 < ∞
0,
f(x; 0, 02) = {02
else where
If 8, = 0,
i) show whether or not E, X, is a minimal sufficient statistic for 02.
ii) Show whether or not E, Xt is a pivotal quantity. Give two reasons why or
why not it is a pivotal quantity.
iii) What is the distribution of E, X;.
Transcribed Image Text:d) Suppose that X,,X2, ., X, is a random sample from a distribution with probability density function: x-01 if x 2 0, and – 0o < ®2 < ∞ 0, f(x; 0, 02) = {02 else where If 8, = 0, i) show whether or not E, X, is a minimal sufficient statistic for 02. ii) Show whether or not E, Xt is a pivotal quantity. Give two reasons why or why not it is a pivotal quantity. iii) What is the distribution of E, X;.
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