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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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    Solution Summary

    The solution gives detailed steps on finding the mean and method of moment estimate of uniform distribution.