Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N)-N , N ; w...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N) X1,2.. N; where N 1,2,.3,.. We wish to test the hypotheses: H,: N- 30 versus H,: N <30. Our critical region is of the form R {x : x < k} , where k is an integer. Find the largest value of k such that the test is level α 0.05. a) β (10) Using this k, what is the chance of...
Suppose that a random sample of size 36, Y1,Y2,...,Y36, is drawn from a uniform pdf de ned over the interval (0, θ), where θ is unknown. Set up a large- sample sign test for deciding whether or not the 25th per- centile of the Y -distribution is equal to 6. Let α = 0.05. With what probability will your procedure commit a Type II error if 7 is the true 25th percentile?
---------------------------------------------------------------------------------------------------------------------------------------------------------- Reference: 11.2.3 Suppose that X. , X are iid MI, σ2) where σ (E 9t*) is the unknown parameter but μ(€ 9) is assumed known. With preassigned α ε (0. 1), derive a level α LR test for a null hypothesis Ho : σ.-a> 0) against an alternative hypothesis H, : σ2 σ1 in the implementable form. {Note: Recall from the Exercise 8.5.5 that no UMP level a test exists for testing Ho versus 8.5.5 Let X, X, be...
8.4.12 Suppose that X, .., Y, are iid random variables having the ernoulli(p) distribution where p e (0, 1) is the unknown parameter. With (0, l ), derive the randomized UMP level α test for l, P-Po p reassigned oE versus H p Po where p, is a number between 0 and 1 8.4.12 Suppose that X, .., Y, are iid random variables having the ernoulli(p) distribution where p e (0, 1) is the unknown parameter. With (0, l ),...
9.A discrete random variable X has pdf of form f(x) x-1,2, ...n, and zero otherwise. A) Find c. B) Find an expression for f (x). 10. If f(x) Cx for x 1,2,3, ... pq*-1 otherwise Find an expression for F(x). Show your work! 9.A discrete random variable X has pdf of form f(x) x-1,2, ...n, and zero otherwise. A) Find c. B) Find an expression for f (x). 10. If f(x) Cx for x 1,2,3, ... pq*-1 otherwise Find an...
2. (7 pts) Given the pdf f(x,0)- statistic Ymaz to test Ho : θ, θ > 0, .Take a sample of size 3 from this pdf. Use the 4,0 y 5 versus HA : θ > 5. (a) What is the decision rule when a 0.05. (b) Suppose θ-7, what is the Type II error for the test in part (a). 2. (7 pts) Given the pdf f(x,0)- statistic Ymaz to test Ho : θ, θ > 0, .Take a...
3. Suppose that X (X...,X) is a random sample from a uniform distribution of the interval [0,0], where the value of ? is unknown, and it is desired to test the hypotheses H: 0>2 [5] (a) Show that the uniform family f(x;0)-(1/0)1 om(r) : ? > 0 maxi-isnXi. has a monotone likelihood ratio in the statistic T(X)- X. whereX (n) [5] (b) Find a uniformly most powerful (UMP) test of level ? for testing Ho versus HI
MA2500/18 8. Let X be a random variable and let 'f(r; θ) be its PDF where θ is an unknown scalar parameter. We wish to test the simple null hypothesis Ho: 0 against the simple alternative Hi : θ-64. (a) Define the simple likelihood ratio test (SLRT) of Ho against H (b) Show that the SLRT is a most powerful test of Ho against H. (c) Let Xi, X2.... , X be a random sample of observations from the Poisson(e)...
A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS θ for the purpose of testing Ho : θ-2 against H, : θ < 2 at α : 0.10 level of significance. Suppose the decision rule is to be based on Xmax, the largest order statistic. What would be the probability of committing a Type II error when θ 1.7. A random sample of size n -8 is drawn from uniform pdf f(x,θ)- , 0-XS...
14.2.10. Suppose that a random sample of size 36, Y, Y2, ..., Y36, is drawn from a uniform pdf defined over the interval (0, 0), where 0 is unknown. 'Set up a large- sample sign test for deciding whether or not the 25th percentile of the Y-distribution is equal to 6. Let a =0.05. With what probability will your procedure commit a Type II error if 7 is the true 25th percentile?