Let Xi, c〉0. Xn be i.i.d. from the Pareto distribution Pa(θ.e), θ 〉 0 Derive a ÙNIP test of size α for testing Ho : θ-Bo, c co versus 0, C > Co Let Xi, c〉0. Xn be i.i.d. from the Pareto di...
Let Xi, c〉0. Xn be i.i.d. from the Pareto distribution Pa(θ.e), θ 〉 0 Derive a ÙNIP test of size α for testing Ho : θ-Bo, c co versus 0, C > Co Let Xi, c〉0. Xn be i.i.d. from the Pareto distribution Pa(θ.e), θ 〉 0 Derive a ÙNIP test of size α for testing Ho : θ-Bo, c co versus 0, C > Co
xn be i.id. from the Pareto distribution Pa(θ, c), θ Let Xi 0 (a) Derive a ÚMP test of size α for testing Ho : θ θ when c is known. versus Hi : xn be i.id. from the Pareto distribution Pa(θ, c), θ Let Xi 0 (a) Derive a ÚMP test of size α for testing Ho : θ θ when c is known. versus Hi :
3. Let Xi, ,X, be i.id. from a normal distribution N(1,0), for θ > 0, Find a UMP test of size α for testing Ho : θ < θο versus H1 : θ > θο. 3. Let Xi, ,X, be i.id. from a normal distribution N(1,0), for θ > 0, Find a UMP test of size α for testing Ho : θ θο.
Suppose that Xi, X2,..., Xn is an iid sample from r > 0 where θ 0. Consider testing Ho : θ-Bo versus H1: θ (a) Derive a size α likelihood ratio test (LRT). (b) Derive the power function P(0) of the LRT. θο, where θο is known. (c) Now consider putting an inverse gamma prior distribution on θ, namely, 1 00), a 4a where a and b are known. Show how to carry out the Bayesian test (d) Is the...
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) )
Can anyone help me with this problem? Thank you! 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1: θ θο. (a) For a sample of size n, find a uniformly most powerful (UMP) size-a test if such exists. (b) Take n-?, θ0-1, and α-.05, and sketch the power function of the UMP test. 7. Let X1,.. , Xn denote a random sample from (1-9)/0 x; Test Ho: θ Bo versus H1:...
1. )To test Ho: X ~ N(θ, l), against Hi : X ~ C(1,0), a sample of size 2 is available on X. Find a UMP invariant test of Ho against Hi 2. Let Xi, X2, , Xn be a sample from PA) Find a UMP unbiased size test 1. )To test Ho: X ~ N(θ, l), against Hi : X ~ C(1,0), a sample of size 2 is available on X. Find a UMP invariant test of Ho against...
Suppose Xi and X2 are iid from 0, otherwise, where θ 0, and consider testing Ho : θ 1 versus H1 : θ 1 . We have two tests: where 0<c<1 (a) Show that the power functions of the two tests are A(0)-1-(0.9)θ and β2(0)-1 + d|θ Inc-1), respectively. (b) Calculate the size of the φι test. Then, find the value of c that gives the same size for the φ2 test. (c) Is фг a most powerful test of...
Let Xi,.., Xn be a sample from Poisson(0) distribution. Consider testing where θ° is a given constant. Use LRT to derive the general form of the union- intersection rejection region in its simplest form.
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: