Question

A salesperson for a medical device company has three appointments on a given day. At the first appointment, he believes that he has a 70% chance to make the deal. On the other hand, to make the deal at the second and third appointments depends on previous appointment. He thinks he only has a 50% chance if the previous appointment is successful and 40% chance if not. (For Example: if first appointment is not successful the chance of being successful at second appointment is 40%. If 2nd appointment is successful the chance of being successful at third appointment is 50%) • From first appointment he can earn $1000 commission if successful. • From second and third appointments, he can make $1500 commission if successful. • Let X be the commission earned after three appointments? • Let Y be number of successful deals

. a) Find E(X) and E(Y)

b) Find Var(X) and Var (Y)

c) Find COVARIANCE (x,y) and CORRELATION(x,y)

d) Show that X and Y are not independent.

e) Optional: Find average commission per successful appointment (E( X/Y| Y>0))

Answer 1