Question: Please show the work. Suppose that X is a random variable with density function f(:1:,0) = (3('39), 0 00. vi) Hence or otherwise justify that

Please show the work.

Suppose that X is a random variable with density function f(:1:,0) = (3('39), 0 00. vi) Hence or otherwise justify that X (1) is a consistent estimator of 0. b) Now suppose that X (1), X (2), X (3), X (4), X (5) are the order statistics of a random sample of size ve from this distribution. Let the observed value of X (1) be 39(1). The test rejects H0 : t9 = 2 and accepts H1 : 0 7E 1 when either 55(1) 2 2 or 31(1)

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