The weekly number of luxury and compact cars sold by "Honest" Abe Smith at the Auto Mart, a local car dealership, can be represented as the outcome of a bivariate random variable \((X, Y)\) with the nonzero values of its joint probability density function given by

\(\mathrm{Al}\) receives a base salary of \(\$ 100 /\) week from the dealership, and also receives a commission of \(\$ 100\) for every compact car sold and \(\$ 200\) for every luxury car sold.

(a) What is the expected value of the weekly commission that \(\mathrm{Al}\) obtains from selling cars? What is the expected value of his total pay received for selling cars?

(b) What is the expected value of his commission from selling compact cars? What is the expected value of his commission from selling luxury cars?

(c) Given that Al sells four compact cars, what is the expected value of his commission from selling luxury cars?

(d) If 38 percent of \(\mathrm{Al}^{\prime}\) 's total pay goes to federal and state taxes, what is the expected value of his pay after taxes?

Transcribed Image Text:

X Y 0 1 0 201 .15 1 .10 075 .0.3 .03 23 2 .05 3 .04 2 3 4 075 .05 .03 .04 .03 .02 .02 .01 .01 .02 .01 .01