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