A circle of radius r has area A = r 2. If a random circle has a radius that is uniformly

Chapter 4, Problem 4.43

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QUESTION:

A circle of radius r has area A = r 2. If a random circle has a radius that is uniformly distributed on the interval (0, 1), what are the mean and variance of the area of the circle?

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QUESTION:

A circle of radius r has area A = r 2. If a random circle has a radius that is uniformly distributed on the interval (0, 1), what are the mean and variance of the area of the circle?

ANSWER:

Step 1 of 3

Given that,

Area of the circle, . Here radius, . We want to find the mean and variance of the area of the circle.

Let us assume that,  be the random variable with probability density function ; and  is a real valued function, then,

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