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Homework 9 Problem 1: Let's say that we are examining a game that has a \"spinner\" as one of its play pieces (kind of like \"The Game of Life\"). This spinner is an example of discrete uniform distribution with a minimum of 1 o 2_ % = 8.25. Let X, represent the result of the first spin on the spinner and X, represent the second result. Assume Cov(X;,X;) = 0. and a maximum of 10. The mean is 5.5 and the variance is a. Whatis E(X; +X;)? b. Whatis Var(X, + X,)? c. Whatis Var(X, X,)? d. If we doubled the value of the spinner, what would the new variance be? Problem 2: Let's say | want to compare the proportion of people that have played Monopoly to the proportion of people that have played Settlers of Catan. In a random sample of 70 people, 20 had played Monopoly. In a random sample of 100 people, 10 had played Settlers of Catan. a. Create a 95% confidence interval for pyonopory Pcatan- b. Interpret the confidence interval. c. Can we conclude that the proportions are the same