(Solved): 1. (12 points) Corduroy and Tootie each run their own hedge fund, although it isthought that they sh ...

1. (12 points) Corduroy and Tootie each run their own hedge fund, although it isthought that they share investment strategies because they are such close friends.It is found that they both make money 70 percent of the time and they both losemoney 30 percent of the time, but Corduroy never makes money when Tootieloses money and Tootie never makes money when Corduroy loses money. Letrepresent when Corduroy makes money andwhen he loses money. X 0 X 1 Similarly, letmoney. Y 1 represent when Tootie makes money and Y 0 when he loses a. (2 points) Calculate the marginal probability distributions for X and Y. b. (2 points) Calculate the expected values of X and Y. c. (2 points) Calculate the variances of X and Y. d. (2 points) Calculate the covariance of X and Y. e. (2 points) Calculate the correlation for X and Y. f. (2 points) Based on your answer to part (h), do you believe that Corduroy andTootie share investment strategies? 2. (10 points) The random variable X follows a normal distribution with ? = 0.2 and?2 = 0.0025.a. (2 points) Calculate b. (2 points) Calculate Pr X 0.4 . Pr 0.15 X 0.28 . c. (2 points) Calculate Pr X 0.1 . d. (2 points) Calculate the value of x such that e. (2 points) Calculate the values ofsuch that Pr x0 X x1 0.34 . x0 and x1 Pr X x 0.025 . that are equidistant from the mean 3. (4 points) The amount of time that Professor Hapoleon spends with studentsduring office hours averages 10 minutes and follows an exponential distribution. a. (2 points) Calculate the probability that he spends more than 20 minutes with agiven student. b. (2 points) Calculate the probability that he spends between 10 and 15 minutes with agiven student.