The information associated with the maximum likelihood estimator of a parameter 0 is 4n, where n is the number of observations. Calculate the asymptotic variance of the maximum likelihood estimator of 20 . (A) (B) (C) (D) 8n (E) 16n
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- Suppose X and Y are independent random variables with the same mean µ but possibly different variances σx2 and σy2. Imagine that X and Y are the averages of independent samples of size n1 and n2, respectively, taken from populations with the same mean µ and the same variance σ2. Apply below to identify the α that minimizes and the minimum value. Be sure to simplify both the new estimator and the minimum variance. Interpret the result. The variance of αX+(1-α)Y, which also has mean µ, is minimized with α=σy2/(σX2+σy2).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)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)
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- A random variable X is uniform from 4 to 8. A Gaussian random variable Y has mean of 10. Approximate the variance ofYY if only 2.5% of its elements is a subset of X.If y1, y2,..., ym be a random sample taken from a normal distribution with parameters x and n× n, then the likelihood equation isTwo 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?
