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The Mean and Method of Moment Estimate of Uniform Distribution

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Please see the attached file for probability questions.
1. Consider the probability density function for the uniform distribution on the range (a,b),
b > a,

fx (x) = (b - a)^-1, a < x < b.

a) Sketch the probability density function fx (x).
b) Derive the mean of the distribution in terms of a and b.
c) Given a random sample of n observations, x_1, x_2,...,x_n from this distribution, complete the following.
i) Assume that a = 0. Use the method of moments to find an estimate for b.
ii) Assume that a = -b. Use the method of moments to find an estimate for b.

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