Question

Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that...

Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possibly infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x).

Homework Answers

Answer #1

Given pdf and CDF . Now the property of pdf is

.

Now

That is is a strictly increasing function of over the interval .

Given the transformation .

The pdf of is

The distribution of uniform in the interval

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