X is Еxp(). (7) Find the variance of when The correct answer is 1/2 212 2/22 1/22 None of the above N/A (Select One)
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- A park ranger is searching for bears in a region of the park where on average there are 5 bears per square mile. The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region. The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear. What is the variance in the number of bears he will find in a 5 square mile region of the park?A manufacturer of cigarettes wishes to test the claim that the variance of thenicotine content of the cigarettes the company manufactures is equal to0.638 milligram. The variance of a random sample of 25 cigarettes is 0.930milligram. At α = 0.05, test the claim.The profit for a new product is given by Z = 3X-Y -5. X and Y are independent random variables with Var(X) = 1 and Var(Y) =2 what is the variance of Z?
- Two different plasma etchers in a semiconductor factory have the same mean etch rate μ. However, machine 1 is newer than machine 2 and consequently has smaller variability in etch rate. We know that the variance of etch rate for machine 1 is σ12, and for machine 2, it is σ2 = σ 2 12 a . Suppose that we have n1 independent observations on etch rate from machine 1 and n2independent observations on etch rate from machine 2.(a) Show that ˆμ = +− α α X X ( ) 1 2 1 is an unbiased estimator of μ for any value of α between zero and one.(b) Find the standard error of the point estimate of μ in part (a).(c) What value of α would minimize the standard error of the point estimate of μ?(d) Suppose that a = 4 and n n 1 2 = 2 . What value of α would you select to minimize the standard error of the point estimate of μ? How “bad” would it be to arbitrarily choose α= . 0 5 in this case?In a fish restaurant, population variance for fish to go bad is at least 4 days. After buying a new cooling system, its expected to be less than 4 days. After buying the new cooling system, 10 fish are tested and with an average of 8 days without going bad with a population variance of 3 days. Test with 95 confidince if the population variance is really less than 4 days. (use chi square please)Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.
- A normally distributed random variable has a mean of 449: a. If a score of 325 has a standard normal score - 1.38, compute for the variance of the X.b. If a score has 404 is three standard deviations below the mean, find standard deviation of X.c. If a score of 433 lies two standard deviations above the mean, find the variance of X.In a fish restaurant, population variance for fish to go bad is at least 4 days. After buying a new cooling system, its expected to be less than 4 days. After buying the new cooling system, 10 fish are tested and with an average of 8 days without going bad with a population variance of 3 days. Test with 95 confidince if the population variance is really less than 4 days. (use chi square test for the lower-side by using the formula and not the excel please)For a sample of 10 individuals, a researcher calculates residuals for the relationship between “number of delinquent friends” and “number of prior arrests” and finds that the positive residuals = 125. The researcher then collects a second sample of 10 individuals and calculates the residuals on the same two variables and discovers the sum of the positive residuals = 75. What can you conclude about the strength of the relationship between “number of delinquent peers” and “number of prior arrests” across these two random samples? How are they similar/different?
- Suppose that X1, ..., Xn are random variables such that the variance of each variable is 1 and the correlation between each pair of different variables is 1/4. Determine Var (X1 + ...+Xn).The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…Two random samples of sizes 10, 13 are taken from types of plastics and tested for breaking strength. The test result is that the average strength of the first type 175 and the average strength of the second type is 160. It is known that the two samples have variances 12, 16. The company decides not to use the first type unless its strength exceeds that of second type by at most 9. Should they use the first type or not? (Assume a=0.1)
