A release-checked easy problem for training Uniform, Expected Value/LOTUS.
Question
Lewis says that he can determine the area of a rectangle just by looking at it. Suppose that Lewis' error in measuring the length of the rectangle is a $\unif{-10}{10}$ random variable, and his error in measuring the width of the rectangle is a $\unif{-5}{10}$ random variable, and his errors in measuring these two quantities are independent. If Lewis tries to measure the area of a rectangle that is $100$ units long and $50$ units wide, what is the expected area he will give?
Practice focus
This Probability problem is tagged Uniform, Expected Value/LOTUS. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.