8. Let the n-vector y be a vector of mutually independent realizations from the uniform distribution on the interval (a, ẞ), that is, yi ~ U(a, B), i = 1, 2, ..., n. (a) What is the likelihood function of a and B (b) Find the MLEs â and B. (c) Suppose that the true values of the parameters are ao = 0 and B0 = 1. Show that the CDF of â is F(a) = Pr[â ≤ a] = 1 − (1 − a)". Use this result to show that n(â ao) is asymptotically exponentially distributed.

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8. Let the n-vector y be a vector of mutually independent realizations from the uniform
distribution on the interval (a, ẞ), that is, yi ~ U(a, B), i = 1, 2, ..., n.
(a) What is the likelihood function of a and B
(b) Find the MLEs â and B.
(c) Suppose that the true values of the parameters are ao = 0 and B0 = 1. Show that
the CDF of â is F(a) = Pr[â ≤ a] = 1 − (1 − a)". Use this result to show that
n(â ao) is asymptotically exponentially distributed.
Transcribed Image Text:8. Let the n-vector y be a vector of mutually independent realizations from the uniform distribution on the interval (a, ẞ), that is, yi ~ U(a, B), i = 1, 2, ..., n. (a) What is the likelihood function of a and B (b) Find the MLEs â and B. (c) Suppose that the true values of the parameters are ao = 0 and B0 = 1. Show that the CDF of â is F(a) = Pr[â ≤ a] = 1 − (1 − a)". Use this result to show that n(â ao) is asymptotically exponentially distributed.
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