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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(choose chapter or problem)
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?
Questions & Answers
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,