State the following (a) Weak Law of Large numbers (b Bernoulli's Law of Large numbers.
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- What is the total effect on the economy of a government tax rebate of $500 to each household in order to stimulate the economy if each household will spend of the rebate in goods and services?Suppose you toss a fair coin 10,000 times. Should you expect to get exactly 5000 heads? Why or why not? What does the law of large numbers tell you about the results you are likely to get? Should you expect to get exactly 5000 heads? Why or why not? What does the law of large numbers tell you about the results you are likely to get?Evaluate using Bernoulli's.
- State either the law of large numbers, the central limit theorem, or the law of rare events.The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and 84 preserved Etruscan male skulls was analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, “The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones.” In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O’Connor, eds., Little, Brown&Co., 1959] a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples. b. Based on your results from part (a), which would you be inclined to use to…