The accompanying table shows for credit card holders with one to three cards the joint probabilities for the number of cards owned (X) and number of credit purchases made in a week (Y). Complete parts a through c below. Number of Number of Purchases in Week (Y) Cards (X) 0 1 2 3 4 0.06 0.14 0.08 0.06 0.03 0.02 0.08 0.07 0.09 0.06 0.01 0.04 0.06 0.07 0.13 1 a. For a randomly chosen person from this group, what is the probability distribution for the number of purchases made in a week? Number of Number of Purchases in Week (Y) Cards (X) 0 1 X (Type integers or decimals rounded to two decimal places as needed.) b. For a person in this group who has three cards, what is the probability distribution for number of purchases made in a week? Number of Number of Purchases in Week (Y) Cards (X) 0 3 3 (Type integers or decimals rounded to two decimal places as needed.) c. Are the number of cards owned and number of purchases made statistically independent? O A. No, because the joint probabilities are the products of the marginal probabilities. Statistical independence means that for all pairs of values x and y, P(x,y)=Px)P(y). OB. Yes, because the joint probabilities are the products of the marginal probabilities. Statistical independence means that, for all pairs of values x and y. Plx,y)=P(x)P(y) OC. Yes, because the joint probabilities are not the products of the marginal probabilities Statistical independence means that for all pairs of values x and y, P(xy) # P(x)P(y) OD. No, because the joint probabilities are not the products of the marginal probabilities Statistical independence means that for all pairs of values and y, P(x,y)=P(x)PV). The accompanying table shows for credit card holders with one to three cards the joint probabilities for the number of cards owned (X) and number of credit purchases made in a week (Y). Complete parts a through c below. Number of Number of Purchases in Week (Y) Cards (X) 0 1 2 3 4 0.06 0.14 0.08 0.06 0.03 0.02 0.08 0.07 0.09 0.06 0.01 0.04 0.06 0.07 0.13 1 a. For a randomly chosen person from this group, what is the probability distribution for the number of purchases made in a week? Number of Number of Purchases in Week (Y) Cards (X) 0 1 X (Type integers or decimals rounded to two decimal places as needed.) b. For a person in this group who has three cards, what is the probability distribution for number of purchases made in a week? Number of Number of Purchases in Week (Y) Cards (X) 0 3 3 (Type integers or decimals rounded to two decimal places as needed.) c. Are the number of cards owned and number of purchases made statistically independent? O A. No, because the joint probabilities are the products of the marginal probabilities. Statistical independence means that for all pairs of values x and y, P(x,y)=Px)P(y). OB. Yes, because the joint probabilities are the products of the marginal probabilities. Statistical independence means that, for all pairs of values x and y. Plx,y)=P(x)P(y) OC. Yes, because the joint probabilities are not the products of the marginal probabilities Statistical independence means that for all pairs of values x and y, P(xy) # P(x)P(y) OD. No, because the joint probabilities are not the products of the marginal probabilities Statistical independence means that for all pairs of values and y, P(x,y)=P(x)PV)
