Let X and Y be two discrete random variables with a joint probability distribution described in the following table. X=0 means tomorrow is going to rain, and X =1 means tomorrow will not rain; Y=0 means Sandy will take a long commute to shop tomorrow, and Y=1 means Sandy will take a short commute to shop tomorrow. Long commute (Y=0) Short commute (Y=1) Total Rain (X=0) 0.15 0.50 0.65 No rain (X=1) 0.10 0.25 0.35 Total 0.25 0.75 1.00 (a) [7.5 pts] Interpret the number in the first cell "0.15". (b) [7.5 pts] What is the probability that tomorrow will rain? (c) [12 pts] What are the respective expected values of X and Y, show your work to get full points. (d) [8 pts] Calculate E(Y| X=0) and E(Y| X=1), show your work to get full points