A manufacturer produces items with a rectangular base. Let random variables denote the respective length(x) and width(y) of the rectangle (in cm).

Question

Suppose x and y are independent with the following parameter values.

E(x)= 2, Var(x)= 0.12, E(y)= 7, Var(y)= 0.34

The perimeter is 2x + 2y. (Round to 4 decimal places if needed)

a) What is the mean of the perimeter of the rectangle?

b) What is the standard deviation of the perimeter of the rectangle?

Answer 1

use rules:

mean(ax + by) = a*mean(x) + b*mean(y)

var(ax + by) = a^2*var(x) + b^2*var(y)

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mean (2x + 2y) = 2 * mean(x) + 2 * mean(y) = 2 * 2 + 2 * 7 = 18 cm

var(2x + 2y) = 4*var(x) + 4*var(y) = 4*0.12 + 4*0.34 = 1.84 cm

std(2x + 2y) = sqrt(1.84) = 1.36 cm