5. The daily price/gallon and quantity sold (measured in millions of gallons) of a lubricant sold on the wholesale spot market of a major commodity exchange is the outcome of a bivariate random variable (P,Q) having the joint probability density function fðp; qÞ ¼ 2 pepq I½:5;1 ðpÞIð0;1Þ ðqÞ:

(a) Define the regression curve of q on p.

(b) Graph the regression curve that you have defined in (a).

(c) What is the expected value of the quantity of lubricant sold, given that price is equal to $.75 per gallon?

(d) What is the expected value of total dollar sales of lubricant on a given day?