Let U be a Uniform r.v. on the interval (-1, 1) (be careful about minus signs).

(a) Compute , , and .

(b) Find the CDF and PDF of . Is the distribution of Uniform on (0, 1)?

(a) Compute , , and .

(b) Find the CDF and PDF of . Is the distribution of Uniform on (0, 1)?

Solution: Let G(t) be the CDF of U^2. G(t) = square root of t. G'(t) = 0.5t^-0.5 is the PDF of U^2. The distribution of U^2 is not Uniform on (0, 1) as the PDF is not a constant on this interval (it is an example of a Beta distribution, which is another important distribution in statistics and will be discussed later).
Consult iTunes course for detailed solutions.

Copyright © 2011 Stat 110 Harvard.
Website layout by former Stat110'er.