5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we...
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if x is a single observation taken from population has probability density Among possible simple likelihood ratio tests for testing Ho : θ 0 versus HI :6-1, find the Most powerful test which minimizes the sum of the sizes of the Type I and Type II erors
if x is a single observation taken from population has probability density Among possible simple likelihood ratio tests for testing Ho : θ 0 versus HI :6-1,...
i need the solution with steps
If x is a single observation taken from population has probability density function fx(x,0)-28x + 1-0, 0 < x < 1,-1 θ 1 Among all possible simple likelihood ratio tests for testing s the Ho:0 0 versus H:0-1, find the Most powerful test which sum of the sizes of the Type I and Type II errors
If x is a single observation taken from population has probability density function fx(x,0)-28x + 1-0, 0
N(0,02). We wish to use a 1. [18 marks] Suppose X hypothesis single value X = x to test the null Ho : 0 = 1 against the alternative hypothesis H1 0 2 Denote by C aat the critical region of a test at the significance level of : α-0.05. (f [2 marks] Show that the test is also the uniformly most powerful (UMP) test when the alternative hypothesis is replaced with H1 0 > 1 (g) [2 marks Show...
5. Suppose Y represents a single observation from the probability density function given by: Soyo-1, 0, 0<y<1 elsewhere Find the most powerful test with significance level a=0.05 to test: HO: 0=1 vs. Ha: 0=2.
Problem 2: Consider two probability density function on [0,1] : fo(x) = 1 and fi(x) = 2x (a) Construct the most powerful test for Ho : X~ fo against H:Xfi with the signifi- cance level x = 0.1 (b) Find its power. (c) Suppose we observe X= 5/6. What is the p-value of the test in 2(a).
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4 Let X be a single observation from the density f(x; 0)= Ox® -110, 1)(x), where 0 >0. (a) In testing Ho: 0 <1 versus H 1:8 > 1, find the power function and size of the test given by the following: Reject H , if and only if X > . (6) Find a most powerful size-a test of Ho:8=2 versus H 1:0= 1. (c) For the loss function given by [(do; 2) = f(d1;...
You have observed one observation X from a distribution with probability density function fx (x) and support X = {x : 0 〈 x 〈 1} (a) Derive the most powerful α 0.05 test for testing Ho : fx(x) = 2x 1 (0 < x < 1) versus H1 : fx (x) = 5c4 1 (0 〈 x 〈 1). Be sure to give the rejection region explicitly. (b) Compute the power of the test
You have observed one observation...
Problem 5 (15pts). Suppose that we observe a random sample X. from the density Xn 1 0 2 0, else, where m is a known constant which is greater than zero, and 0>0. (a) Find the most powerful test for testing Ho : θ Bo against b) Indicate how you would find the power of the most powerful test when θ-e-Do not perform (c) Is the resulting test uniformly most powerful for testing Ho :0-00 against Ha :e> et Explain...
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
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4. A single observation Y from a population with /(1)-ete i. О < บく1, is made. (a) Find the most powerful > 0.90 İOO 0.025-level tavit for H0 : e-3 vs. Hai θ-5. (b) For the test in (a), tind power(5). (b) 0.04132 Ans. (a)