At the power plant, rectangles that are 2 m long and 1 m wide are produced. The length of the objects is measured by the worker Howard, and the width, irrespective of Howard, is measured by the worker Rachel. The average error is zero for both, but Howard allows a standard measurement error (standard deviation of length) of 3 mm, and Rachel allows a standard error of 2 mm.
a) Find the mathematical expectation of the area of the resulting rectangle.
b) Find the standard deviation of the area of the resulting rectangle in centimetres squared.