Problem 7 For each of the following random variables, find P(X5), P(2

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13) (3 points each) Suppose X and Y are independent random variables each having expected value 5 and standard deviation 3. Calculate d) If you were told that Cov(X,Y) = 4, and that X and Y are not independent, what would Var(X-Y) be?

3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.

17. In Problem 11 from the previous section, westated that the damage amount is normally distributed. Suppose instead that the damage amount istriangularly distributed with parameters 500, 1500,and 7000. That is, the damage in an accident canbe as low as $500 or as high as $7000, the mostlikely value is $1500, and there is definite skewnessto the right. (It turns out, as you can verify in @RISK,that the mean of this distribution is $3000, thesame as in Problem 11.) Use @RISK to simulatethe amount you pay for damage. Run 5000 iterations. Then answer the following questions. Ineach case, explain how the indicated event wouldoccur.a. What is the probability that you pay a positiveamount but less than $750?b. What is the probability that you pay more than$600?c. What is the probability that you pay exactly $1000(the deductible)?