I HOPE ITS HELPFUL TO YOU IF YOU HAVE ANY DOUBTS PLS COMMENTS BELOW..I WILL BE THERE TO HELP YOU ...ALL THE BEST
I HOPE YOU UNDERSTAND..PLS RATE THUMBS UP ITS HELPS ME ALOT..
THANK YOU...!!
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N) X1,2.. N;...
Suppose X is Discrete Uniform(N). N is unknown. Thus, the pdf of X is given by f, (x:N)-N , N ; where N-|, 2,3, x# 1,2, 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) b) Using this k, what is the chance of type II...
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?
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...
Suppose that the covariates Xj,i for i 1, 2, , n and j 1, 2, , indicator variables for a single categorical variable in the manner covered in the course. Thus, suppose that for each individual i = 1,2,…,n we have that X1.i, X2.i,...,Xd,i this one is equal to the number 1. Let Bk be the (A , . . . , β 1), the minimizer of L (bi , b2, . . . ,勿of eq. (B. = Yn.(k), where...
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)...
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?
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 ),...
FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-Y )2-100. obtain a 99% confidence interval for σ of having the form b, 0o) for some number b (No derivation needed). (b) 60 random points are selected from the unit interval (r:0 . We want...