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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?
Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 90% confidence that the sample mean is within 8 IQ points of the true mean.
a hotly disputed proposition x will be on the ballot in november elections. a poll of n1 100 people shows that p1 50
Represent the data relating to the average travel times in a histogram and represent the data relating to the percentage of workers using public transportation in a stem and leaf plot.
a charity receives 1700 contributions. contributions are assumed to be independent and identically distributed with
What alternative would be chosen according to expected utility?
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The singular form of the word "dice" is "die". Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What's the probability of getting a three at the third time?
What do confidence intervals represent? What is the most controllable method of increasing the precision of or narrowing the confidence interval?
damien is 68 inches tall. use the equation of the regression-line exactly as given in the first question to predict the
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