Concept explainers
Computer plot graphs like Figure 8.2 but with
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward1.2 number 12 reviewarrow_forward
- An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poissonrandom variable with λ = 7.5. (a) What is the probability that at most 5 cars per year will experience a catastrophe?(b) What is the probability that more than 1 car per year will experience a catastrophe?arrow_forwardIf the alleles A and B of the cystic fibrosis gene occur in a population with frequencies p and 1 - p (where pis between 0 and 1), then the frequency of heterozygous carriers (carriers with both alleles) is 2p(l - p). Which value of p gives the largest frequency of heterozygous carriers?arrow_forwardSuppose the index model for the excess returns for stocks A and B is estimated with the following results: R = 1.0% + 0.9Ru+ eA Rg = -2.0% + 1.1Ru+ og %3! a(ea) - 30% o(eg) = 10% Find the standard deviation of each stock and the covariance between them. A- BI !!arrow_forward
- Can you give a scenario for e and f please?arrow_forwardSection 9.4 5.) A die is tossed 120 times. Use the normal curve approximation to the binomial distribution to find the probability of getting the following result. Exactly 17 5's Use the table of areas under the standard normal curve given below Click here to page 1 Click here to view page 2 Click here to view page 3 Click here to page 4 Click here to view page 5 Click here to view page 6arrow_forwardA 157.arrow_forward
- Suppose the time to complete an exam is normally distributed with µ = 40 minutes and σ = 5 minutes. After how many minutes can we expect all but about 3% of the tests to be completed?arrow_forwardAn insurance company has a portfolio of car insurance. For a given period of time, it is assumed that the drivers are classified in two categories: 'good drivers' and 'bad drivers'. The proportion of good drivers is 75% of the total drivers. We also know that the number of claims for a each driver is following Poisson with parameter A where A =1 for good drivers and A = 3 for bad drivers.arrow_forwardGenetic Creutzfeldt-Jakob Disease (gCJD) is a very rare disease, and the number of deaths caused by gCJD each year in the United Kingdom can be modeled using a Poisson distribution with unknown parameter 0. Numbers of gCJD deaths for the period 2005-9 are given in Table 12. A Gamma(11, 2) was selected as a prior for 0. Year Number of deaths Table 12 2005 2006 13 9 2007 2008 2009 9 5 8 (a) State the posterior for parameter 0, given the data and prior above. (b) Calculate the posterior mode for 8, giving your answer to 2 decimal places. (c) Figure 11 shows the prior, likelihood and posterior for 8. Figure 11 10 Prior Likelihood Posterior 15 Comment on the relative contributions of the prior and data to the posterior, justifying your opinion. How have the data affected opinion about ?arrow_forward
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