Assume that pizza is shaped perfectly in the shape of a circ

Assume that pizza is shaped perfectly in the shape of a circle and the expected radius is 12\" with standard deviation of .5\". What is the expected value and variance of the circumference of the pizza? Don\'t forget units with your answer and justify all non-algebraic steps.

Solution

this problem is more than math

because we need the expect value and var of the circunference

we have the expect value and SD of the radius

we know that:

Circunference = pi * Diameter

Diameter = 2*radius

For expected value of circunference

E(X)= 2*12 * pi = 24pi \'\'

we have SD of radius we need variance of radius that is 0.5^2

Var(X) = 2*0.5^2 * pi = 0.5pi \'\'