# Question Problem 4 (2 points) Suppose that X1,..., Xn is a random sample from a probability density function in the one- parameter exponential family. That is ſa(6)b(x )e-[c@)d(a)], u < x < v f(3;6) = otherwise, where a and care functions that do not depend on 2, b and d are functions that do not depend on 0, and u and v are constants that do not depend on 0. Show that h=1d(Xi) is sufficient for 0. 1 Problem 5 (2 points) Let Y1, ..., Yn be a random sample from a uniform distribution on the interval (0,50). Derive the method of moments estimator for 0.

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Transcribed Image Text: Problem 4 (2 points) Suppose that X1,..., Xn is a random sample from a probability density function in the one- parameter exponential family. That is ſa(6)b(x )e-[c@)d(a)], u < x < v f(3;6) = otherwise, where a and care functions that do not depend on 2, b and d are functions that do not depend on 0, and u and v are constants that do not depend on 0. Show that h=1d(Xi) is sufficient for 0. 1 Problem 5 (2 points) Let Y1, ..., Yn be a random sample from a uniform distribution on the interval (0,50). Derive the method of moments estimator for 0.
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Transcribed Image Text: Problem 4 (2 points) Suppose that X1,..., Xn is a random sample from a probability density function in the one- parameter exponential family. That is ſa(6)b(x )e-[c@)d(a)], u < x < v f(3;6) = otherwise, where a and care functions that do not depend on 2, b and d are functions that do not depend on 0, and u and v are constants that do not depend on 0. Show that h=1d(Xi) is sufficient for 0. 1 Problem 5 (2 points) Let Y1, ..., Yn be a random sample from a uniform distribution on the interval (0,50). Derive the method of moments estimator for 0.