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Let Z = X/Y where X and Y have normal densities with mean 0 and standard deviation 1. Then it can be shown that Z has a Cauchy density. (a) Write a program to illustrate this result by plotting a bar graph of 1000 samples obtained by forming the ratio of two standard normal outcomes. Compare your bar graph with the graph of the Cauchy density. Depend- ing upon which computer language you use, you may or may not need to tell the computer how to simulate a normal random variable. A method for doing this was described in Section 5.2. (b) We have seen that the Law of Large Numbers does not apply to the Cauchy density (see Example 8.8). Simulate a large number of experi- ments with Cauchy density and compute the average of your results. Do these averages seem to be approaching a limit? If so can you explain why this might be?
An investigator analyzed the leading digits of the amounts from 200 checks issued by three suspect companies. Calculate the χ2 test statistic. Calculate the χ2critical value
Question 1 In agriculture, a "bumper crop" refers to a particularly productive harvest. If there is a bumper crop for wheat at the same time that more people become allergic to wheat and all else is held constant, what will happen to the equilibri..
What would be a good example of a null and alternative hypotheses for a decision relevant in life? What Type I and Type II errors could occur with your decision-making process?
Each factor level has been replicated three times. The computer value of the F-statistic is F0=3.26. Find bounds on the P-value.
you have purchased five shares of stock in diversified machine tools which has a mean value of 25 and a standard
consider the following minimization problemmin z x1 2x2s.t. x1 x2 3002x1 x2 4002x1 5x2 750x1 x2 0what is the
a company wished to model the number of minutes required to unload shipments of drums of chemicals at its warehouse as
a fast food franchiser is considering building a restaurant at a certain loaction. according to a financial analysis a
if four times as many students pass a statistics course as those who fail and one statistics student is selected at
An analyst wishes to include number of older siblings in family as a predictor variable in a regression analysis of factors affecting maturation in eighth graders. The number of older siblings in the sample observations ranges from 0 to 4.
5 cups of coffee per day with a standard deviation of 1.5. The distribution is normal. What proportion of faculty consume an amount between 4 and 6 cups?
consider a line of regression that fits data points showing crime rate and population for all u.s. cities with
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