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The losses on this policy follow a Pareto distribution with a= 3, () = 2000. Even though all the insureds live in the same building, the losses are independent. You are now setting up a reserve for the cost of these losses. Using the normal approximation, calculate the size of the reserve you should put up if you want to have a 95% probability of having enough money in the reserve to pay all the claims. ANswER: The mean of each loss is ° = 1000 and the variance is 20 0 2 E [X2 ) - E(X] 2 = 2(2000 2 ) -1000 2 = 3,000,000 2 The mean of the sum is the sum of the means, or (100)(1000) = 100,000.
To maximize the covariance, the y's should be in the same order as the x's. The sum of the products is (1)(4)+ (2)(2)+(4)(3)+ (5)(6)+(6)(4) = 74. If the y's were ordered in increasing order, the sum would be (1)(2)+(2)(3)+(4)(4)+(5)(4)+(6)(6) = 80. Xji from each and divide by 5, but since we're just comparing A and B, we won't bother subtracting xji. 21. 98 Thus either 96 or 97 experiments are needed. 4j. (A) An alternative to calculus that is more appropriate for this discrete problem is to note that as n increases, at first expected profit goes up and then it goes down.
645 is a commonly used percentile of the normal distribution, and is listed at the bottom of the table you get at the exam. 3. BERNOUUI SHORTCUT 47 You should internalize the above reasoning so you don't have to write it out each time. Namely, to calculate a percentile of a random variable being approximated normally, find the value of x such that