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