5 . (16 points) Suppose a day trader can buy stock in two companies,Apple and Tesla, each valued at $200 per share and they currently have $600 total to invest. Below you'll nd the probability distribution for the potential daily change in each stock (X denotes Apple and Y denotes Tesla). Au- ska rd- and x Ma) y mar) IMRISM 10 0.20 Inueases 15 0.30 No mm 0 9,15 an chime o 0.60 Decreases .10 mos Decrease: is run a) (4 points) Based on the above probability distribution, nd the mean and standard deviation for returns of one unit of each stock (X and Y). (round to two decimals if necessary) b) (3 points) Below is an incomplete joint distribution for X and '1. Find the values of each blank green cell. Discuss your logic. v=15 V'T-ln' y=o v='15 Mil c) (4 points) Suppose a risk-free savings account pays $0.002 per day for every $1 in the savings account. Calculate the Sharpe Ratio for each possibility: i) you only purchase Apple stock and ii) you only purchase Tesla stock. (round to two decimals if necessary) Which is the preferred investment? Discuss your rationale. d) (5 points) Instead of buying only one company's stock, suppose you can diversify and either buy: Option A (two shares of Apple and one share of Tesla) or Option B (one share of Apple and two shares of Tesla). We're given that the Correlation coefcient between X and. Y is 0.30. Are either of these options preferred to your optimal choice in part (c)? Explain and show all work