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Chapter 5 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
- Let x, x2, ..., Xn be a random sample from a Poisson distribution with parameter 2. Find ML estimator of 2. Also find its variance.arrow_forwardLet Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s2 is known. Find the Score function, the estimating equation and the information matrix.arrow_forwardLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.arrow_forward
- Show that the mean of a random sample of size n from an exponential population is a minimum variance unbi-ased estimator of the parameter θ.arrow_forwardQ11. Let X1,X 2,.,X, be a random sample from a Poisson distribution with parameter 2. (a) Find the Cramer-Rao lower bound for the variance of any unbiased estimator of 1. (b) Find the maximum likelihood estimator (m.l.e.) of å. (c) Is this m.l.e. unbiased and does its variance attain the Cramer-Rao lower bound?arrow_forwardLet X1,…,Xn be i.i.d. Exp(λ) random variables, where λ is unknown.What is the variance and quadratic risk of the unbiased estimator θ^ = n*mini(Xi).arrow_forward
- Let Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s2is known. Find the maximum likelihood estimator of b from first principles.Find the Score function, the estimating equation and the information matrix.arrow_forwardLet Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s^2is known.Find the maximum likelihood estimator of b from first principles.Find the Score function, the estimating equation and the information matrix using GLMarrow_forward13. Let Y,, Y2, ..., Yn denote a random sample from a population with pdf f(yl0) = (0 + 1)yº,0 -1 a) Find an estimator for theta by the method of moments. b) Find the maximum likelihood estimator for theta.arrow_forward
- Find the least square estimate for beta (the slope) given that its y-intercept is 0. Y_i = BetaX_i + e_i where e_i are independent and identically distributed N(0, variance_e) randon variables i = 1,...,2.arrow_forwardThe number of ice creams sold per hour from Mr Fishy’s van is observed to be a Poisson random variable with parameter λ = 8. Each ice cream costs two pounds but Mr Fishy has to pay five pounds per hour for the pitch. What is the variance of his hourly profit (measured in pounds and ignoring all other income and expenses)?arrow_forwardDevelop a random variate generator for a random variable X with the pdf if 0arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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