Homework Answers
3.4 Let X,, X be a random sample of size n from the U(Q,62) distribution, 6,...
3.4 Let X,, X be a random sample of size n from the U(Q,62) distribution, 6, and let Y, and Yn be the smallest and the largest order statistics of the Xs (i) Use formulas (28) and (29) in Chapter 6 to obtain the p.d.f.'s of Y and Y and then, by calculating depending only on Yi and 1,- Part i. (Note: it is not saying to find the joint pdf of Yi and Yn Find their marginal Theorem 13...
1. Let Xi,..., Xn be a random sample from a distribution with p.d.f. f(x:0)-829-1 , 0...
1. Let Xi,..., Xn be a random sample from a distribution with p.d.f. f(x:0)-829-1 , 0 < x < 1. where θ > 0. (a) Find a sufficient statistic Y for θ. (b) Show that the maximum likelihood estimator θ is a function of Y. (c) Determine the Rao-Cramér lower bound for the variance of unbiased estimators 12) Of θ
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show th...
1.(c)
2.(a),(b)
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0 -e λ , X > 0 2) (x...
Let X1, ..., Xn be a sample from a U(0, θ) distribution where θ > 0...
Let X1, ..., Xn be a sample from a U(0, θ) distribution where θ > 0 is a constant parameter. a) Density function of X(n) , the largest order statistic of X1,..., Xn. b) Mean and variance of X(n) . c) show Yn = sqrt(n)*(θ − X(n) ) converges to 0, in prob. d) What is the distribution of n(θ − X(n)).
Let X be a sample of size 1 from a Lebesgue p.d.f. fo. Find a UMP test of size α (0, ) for Ho : θ--θ : θ-0, in the o versus H1 tollowing case: Let X be a sample of size 1 from a Lebesgue p.d.f....
Let X be a sample of size 1 from a Lebesgue p.d.f. fo. Find a UMP test of size α (0, ) for Ho : θ--θ : θ-0, in the o versus H1 tollowing case:
Let X be a sample of size 1 from a Lebesgue p.d.f. fo. Find a UMP test of size α (0, ) for Ho : θ--θ : θ-0, in the o versus H1 tollowing case:
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0), x =...
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0), x = 0, 1, 2, . .. , zero elsewhere, where 0 0s I (a) Find the m. l.e., 6, of 0. X, is a complete sufficient statistic for 0. (b) Show that (c) Determine the unbiased minimum variance estimator of 0.
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0),...
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0), x =...
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0), x = 0, 1, 2, . .. , zero elsewhere, where 0 0s I (a) Find the m. l.e., 6, of 0. X, is a complete sufficient statistic for 0. (b) Show that (c) Determine the unbiased minimum variance estimator of 0.
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0),...
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ ...
difficult……
2and4 thanks
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ....
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ ...
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ. (b) Find an...
Let X be a sample of size 1 from a Lebesgue p.d.f. fe. Find a UMP test of size α (0, ) for Ho : θ-Bo versus Hi : θ-A in the following cases: (a) foo)+( and fo, (x) ) Let X be a sample of size 1...
Let X be a sample of size 1 from a Lebesgue p.d.f. fe. Find a UMP test of size α (0, ) for Ho : θ-Bo versus Hi : θ-A in the following cases: (a) foo)+( and fo, (x) )
Let X be a sample of size 1 from a Lebesgue p.d.f. fe. Find a UMP test of size α (0, ) for Ho : θ-Bo versus Hi : θ-A in the following cases: (a) foo)+( and fo, (x) )
3.4 Let X,, X be a random sample of size n from the U(Q,62) distribution, 6, and let Y, and Yn be the smallest and the largest order statistics of the Xs (i) Use formulas (28) and (29) in Chapter 6 to obtain the p.d.f.'s of Y and Y and then, by calculating depending only on Yi and 1,- Part i. (Note: it is not saying to find the joint pdf of Yi and Yn Find their marginal Theorem 13...
1. Let Xi,..., Xn be a random sample from a distribution with p.d.f. f(x:0)-829-1 , 0 < x < 1. where θ > 0. (a) Find a sufficient statistic Y for θ. (b) Show that the maximum likelihood estimator θ is a function of Y. (c) Determine the Rao-Cramér lower bound for the variance of unbiased estimators 12) Of θ
1.(c)
2.(a),(b)
5. Let Xi,..., X, be iid N(e, 1). (a) Show that X is a complete sufficient statistic. (b) Show that the UMVUE of θ 2 is X2-1/n x"-'e-x/θ , x > 0.0 > 0 6. Let Xi, ,Xn be i.i.d. gamma(α,6) where α > l is known. ( f(x) Γ(α)θα (a) Show that Σ X, is complete and sufficient for θ (b) Find ElI/X] (c) Find the UMVUE of 1/0 -e λ , X > 0 2) (x...
Let X be a sample of size 1 from a Lebesgue p.d.f. fo. Find a UMP test of size α (0, ) for Ho : θ--θ : θ-0, in the o versus H1 tollowing case:
Let X be a sample of size 1 from a Lebesgue p.d.f. fo. Find a UMP test of size α (0, ) for Ho : θ--θ : θ-0, in the o versus H1 tollowing case:
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0), x = 0, 1, 2, . .. , zero elsewhere, where 0 0s I (a) Find the m. l.e., 6, of 0. X, is a complete sufficient statistic for 0. (b) Show that (c) Determine the unbiased minimum variance estimator of 0.
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0),...
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0), x = 0, 1, 2, . .. , zero elsewhere, where 0 0s I (a) Find the m. l.e., 6, of 0. X, is a complete sufficient statistic for 0. (b) Show that (c) Determine the unbiased minimum variance estimator of 0.
362 Suficient Statisties 7.76. Let X, X,.. ,x, be a random sample froma distribution with p.d.f. fix: 0) 0(1-0),...
difficult……
2and4 thanks
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ....
Mathematical Statistics แ (Homework y 5) 1. Let , be a random sample fiom the densit where 0 s θ 1 . Find an unbiased estimator of Q 2. Let Xi, , x. be independent random variables having pdfAx; t) given by Show that X is a sufficient statistic for e f(xl A) =-e- . x > 0 3. Let Xi, , x,' be a random sample from exponential distribution with (a) Find sufficient statistic for λ. (b) Find an...
Let X be a sample of size 1 from a Lebesgue p.d.f. fe. Find a UMP test of size α (0, ) for Ho : θ-Bo versus Hi : θ-A in the following cases: (a) foo)+( and fo, (x) )
Let X be a sample of size 1 from a Lebesgue p.d.f. fe. Find a UMP test of size α (0, ) for Ho : θ-Bo versus Hi : θ-A in the following cases: (a) foo)+( and fo, (x) )
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