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