Answer to Question #440 in Statistics and Probability for Mario

Question

The diameter of the circle is measured approximately. Assuming that its value is uniformly distributed on the interval [a, b], find the distribution of the circle square.

Answer 1

The square of the circle is πd²/4. That is, the distribution function of the circle square is: S = πd²/4, a≤d≤b. The minimum value of the square is πa²/4, the maximum is: πb²/4.