Problem Suppose that X;, i=1, ., n, are iid Bernoulli(p). (a) Show that the variance of the MLE of p attains the Cramér-Rao Lower Bound. (b) For n2 4, show that the product X1X2X3X4 is an unbiased estimator of p, and use this fact to find the best unbiased estimator of p4.
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A: Hi, Thanks for posting. As requested, we'll solve only question #3
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- 2) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.A researcher is using a two-tailed hypothesis test with α = 0.01 to evaluate the effect of a treatment. If theboundaries for the critical region are t = ± 2.845, then how many individuals are in the sample?A. n = 23B. n = 22C. n = 21D. n = 20E. cannot be determined from the information given
- Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?Correlated t tests generally have more power than independent-groups t tests because the former usually have smaller standard errors of the difference between means, making the t value bigger. True False
- If I let X1, X2, . . . , Xn ∼i.i.d Exp(λ) with n > 1. how do I find unbiased estimators for this and computer the mean squared error? which estimattor is betterIf 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?A hypothesis test produces a t statistic of t=2.01.If the researcher is using a two tailed test with x=0.05,how large does the sample have to be in order to reject the null hypothesis?