Let Xi following test is considered: Reject Ho if Y1> 1 or Y1 iid U(0,0 1),...
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...
, Xn iid. N 5. Let Xi, (μ, σ2), μ E R and σ2 > 0 are both unknown. Find an asymp- totically likelihood ratio test (LRT) of approximate size α for testing μ-σ 2 H1:ťtơ2 Ho : versus
, Xn iid. N 5. Let Xi, (μ, σ2), μ E R and σ2 > 0 are both unknown. Find an asymp- totically likelihood ratio test (LRT) of approximate size α for testing μ-σ 2 H1:ťtơ2 Ho : versus
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 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, .Χίο be a sample of iid Bin( 1, θ) random variables, and let e-{i : Σοί HA : θ 0.8. Determine a) the size of this critical region. b) the power of this critical region for 0 0.8. x,2 9} be a critical region for testing Ho:0 0.6 versus
Let Xi, .Χίο be a sample of iid Bin( 1, θ) random variables, and let e-{i : Σοί HA : θ 0.8. Determine a) the size of this critical...
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:...
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:
Suppose that Xi, X2, ..., Xn is an iid sample from the distribution with density where θ > 0. (a) Find the maximum likelihood estimator (MLE) of θ (b) Give the form of the likelihood ratio test for Ho : θ-Bo versus H1: θ > θο. (c) Show that there is an appropriate statistic T - T(X) that has monotone likelihood ratio. (d) Derive the uniformly most powerful (UMP) level α test for versusS You must give an explicit expression...
4) Let Xi , X2, . . . , xn i id N(μ, σ 2) RVs. Consider the problem of testing Ho : μ- 0 against H1: μ > 0. (a) It suffices to restrict attention to sufficient statistic (U, v), where U X and V S2. Show that the problem of testing Ho is invariant under g {{a, 1), a e R} and a maximal invariant is T = U/-/ V. (b) Show.that the distribution of T has MLR,...
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...