Exercise 3 (18 points) The following statistics have recently been reported by the British Columbia government over a week in December 2021 regarding the number of Covid-19 cases in the province, along with people who needed hospitalization because of the virus, and whether these patients were vaccinated or not: . Total number of cases: 3,394 . Not vaccinated: 1,386 . Vaccinated (partially or fully): 2,008 . Hospitalized: 155 (among them, 105 aren't vaccinated and 50 are partially or fully vaccinated) Let X be a random variable equal to 1 if the patient was hospitalized, and 0 otherwise. Let Y be a random variable equal to 1 if the patient was vaccinated (partially or fully), and 0 otherwise. In all the subsequent calculations, round off your results at 3 decimal places. (a.) Based on the statistics above, what is the proportion of cases who got hospitalized? Non hospitalized? (1 point) # type answer here Answer: (b.) What is the proportion of cases who got hospitalized and were vaccinated? Hospitalized and non vaccinated? (4 points) # type answer here Answer: (c.) Complete the following table based on your results in question (a.) and (b.) (all the places marked with a "x"). For instance, think of the probability of X = InY = 0 as the proportion of hospitalized and non vaccinated cases (be very careful that everything matches as these numbers are needed in the subsequent questions). (5 points) Answer: Y/X X=0 X=1 P(Y Y = 0 x X Y =1 XY/X X=0 X=1 P(Y) P(X) X X X (d.) Compute P(X = 1/Y = 1) (call it "pll" in R) and P(X = 1/Y =0) (call it "p10" in R). Show the calculation in R. (2 points) # type answer here Answer: (e.) Compute P(X = 0|Y = 1) (call it "pol") and P(X = 0|Y = 0) (call it "p00"). Show the calculation in R. (2 points) # type answer here Answer: (f.) Compute E(XJY = 1) (call it "Exl" in R) and E(X|Y = 0) (call it "Ex0" in R). Show the calculation in R. (2 points) # type answer here Answer: (g.) Given your answer in (f.) and ignoring the side effects of vaccination, would you rather be vaccinated or not? Explain. (2 points)