(d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) mean = standard deviation = (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal
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- A certain process for producing an industrial chemical yields a product containing two predominant types of impurities. For a certain volume of sample from this process, let X1 denote the proportion of impurities in the sample and let X2 denote the proportion of type I impurity among all impurities found. Suppose the joint distribution of X1 and X2, after investigation of many such samples, can be adequately modeled by the following function: (see picture) a. Calculate the probability that X1 is less than 0.5 and that X2 is between 0.4 and 0.7. b. Show that these random variables are independent.Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter l. a) If X1, X2, . . . , Xn are the times, in minutes, between successive customers selected randomly, estimate the parameter of the distribution. b) b) The randomly selected 12 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.3 error and 4% risk, find the minimum sample size.
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