A collector is selling a quantity of action figures at an online auction. He has 19 cowboy figures. In recent auctions, the mean selling price of similar figures has been $12.48, with a standard deviation of $1.38. He also has 12 Indian figures which have had a mean selling price of $10.35, with a standard deviation of $0.75. His insertion fee will be $0.50 on each item, and the closing fee will be 8.75% of the selling price. He assumes all will sell without having to be relisted. Complete parts a through d. a) Define your random variables, and use them to create a random variable for the collector's net income. Let X; be the price of i" cowboy figure sold, Y; be the price of the i" Indian figure sold. Choose the correct net income below. Net income = (X, + ... + X19 + Y, + ...+ Y12) -31(0.50)-0.0875 (X, + ...+X19 + Y, + ... +Y12) b) Find the mean (expected value) of the net income E(net income) = $(Round to two decimal places as needed.) c) Find the standard deviation of the net income. Ignore the insertion and closing fees in this calculation. SD(net income) = $(Round to two decimal places as needed.) d) Do you have to assume independence for the sales at the online auction? Explain. O A. No. The mean and standard deviation can be found without having to assume independence. O B. Yes, independence is required, but only when there are fewer than 30 data values. O C. Yes, independence must be assumed in order to compute the standard deviation