Problem 87E

The opening prices per share Y1 and Y2 of two similar stocks are independent random variables, each with a density function given by

On a given morning, an investor is going to buy shares of whichever stock is less expensive. Find the

a probability density function for the price per share that the investor will pay.

b expected cost per share that the investor will pay.

Elements of Statistics – Chapter 6 Notes Key Points Density Curves Normal Distribution Standard Normal Curve Standard Normal Table Density Curve A fitted curve in regard to distribution Is ALWAYS ON or ABOVE the horizontal axis Total area under a density curve is always equal to 1 o Density Histogram To determine the density of a class, take the relative frequency and divide by the width of class. AREA = DENSITY x WIDTH Normal Distribution A variable is “normally distributed” if its distribution has the shape of a symmetric curve. o Characterized by its Mean, , and a Standard Deviation, o The Mean