national bank offers payment plans for large purchases (like TV, medical expenses, etc.) for consumers. In theory, usually, there is a trade-off between the interest rate (APR) and payment length, i.e. the longer the payment plan, the higher the interest rate. Let us test this theory by using the data collected from the bank. Let X be the interest rate/APR, and Y be the payment plan. (19 points) X 5% 10% 15% 6 Months 0.2 0.1 0 Y 12 Months 0.1 0.2 0.1 24 Months O 0.1 0.2 61 4 1 of 3 a. Is the random variable Y discrete, continuous, dummy, or approximately continuous? Give a simple explanation b. Calculate the mean and standard deviation of X c. Calculate the covariance of X and Y and use that information, is the theory true that the longer the payment plan, the higher the interest rate? d. Suppose all the large purchases are for an expensive TV of $2,000. The payment plan will also incur a processing fee of $5. Let W be a random variable representing the extra money paid from using the payment plan compared to paying a lung-sum payment of $2,000 from the beginning (which means W includes