5.5.2. Let X1, X2,..., Xn be a random sample of size n from the Poisson distribution, px(k;) n = e-xxk, k k! k = 0,1,.... Show that ✩ = ½✗X; is an efficient estimator for λ. i=1
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- 5. Let (*1, x2, .., rn) be n independent random sample of size n from a uniform distribution on the interval [01,02]; (a) find the c.d.f of, X(1), the minimum order statistic (b) find the c.d.f of, X(n), the maximum order statistic (c) Hence, find the mean and variance of X(1) and X(n)-8.11.) Prove that X, the mean of a random sample of size n from a distribution that is N(0, ¹), -∞0 0, an efficient estimator of 0.7. Let Y₁,...,, denote a random sample from the uniform distribution on the interval (0,0+1). Let: 3₁ = 8 - 12/2 Y 8₂ = Y(n) n n+1 Show that both ₁ and 2 are unbiased estimators of 0. >-{ = [1 0Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage