A local office supply and equipment store, Office Station, sells several different brands of personal digital assistants (PDAs). One of the store's managers has studied the daily sales of its two most popular personal digital assistants, the Palm M505 and the Palm Vx, over the past quarter. In particular, she has used historical data to assess the joint probability distribution of the sales of these two products on a typical day. The assessed distribution is shown in the below table. The manager would like to use this distribution to determine whether there is support for the claim that the sales of the Palm Vx are often made at the expense of Palm M505 sales, and vice versa. Sales of M505 are given in the rows and that of Vx are in the columns. Table M505Vx 0 1 2 3 0 0.01 0.03 0.06 0.09 1 0.02 0.06 0.12 0.09 2 0.03 0.12 0.06 0.09 3 0.04 0.09 0.06 0.03
Q1. What is the probability that the store will not sell any M505s? a) 0.19 b) 0.10 c) 0.29 d) 0.22
Q2. What is the probability that the store will not sell any Vx? a) 0.05 b) 0.10 c) 0.29 d) 0.30
Q3. Are the sales of M505s and Vx independent from each other? a) Yes b) No c) Neither d) Cannot be determined based on the information given in the problem. A manufacturer of television sets sells two principal models. Define X=sales of model A next December (nearest 100,000) and Y = sales of model B next December. The marketing staff estimates that the joint probabilities Px,y(x,y) are y 1 2 3 4 x 1 .030 .055 .070 .075 2 .055 .070 .075 .070 3 .070 .075 .070 .055 4 .075 .070 .055 .030
Q4. Find P(X=1,Y=2) a) 0.03 b) 0.055 c) 0.075 d) 0.070