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4. A researcher is investigating the relationship between the number credit cards owned by a consumer and the number of online purchases made in a week. The joint probability distribution for the number of credit cards owned and number of online purchases made in a week is as follows: Y ( number of online purchases in a week) 0 1 2 0.21 0.09 0.09 X (number of credit cards) WNH 0. 11 0.08 0.16 0.04 0.06 0.16 (a) If a person is randomly selected, what is the expected number of credit cards owned, and the expected number of online purchases made in a week? [4 marks] (b) Find the variance for the number of credit cards owned and the number of online purchases made in a week. Calculate the covariance between the number of credit cards owned and the number of online purchases made in a week. Are these two variables statistically independent? Explain your answer. [9 marks] (c) Do these results indicate that the number of online purchases in a week increase with the number of credit cards owned? Explain your answer. [2 marks