Answer:
Consider two pdfs f(C) and f, (x) which are defined as follows 1 0sxs1 f(x)=16 otherwise and i(x)...
Problem H5 Let X be a single observation (n-1) from the following distribution: f(rle)-o elsewhere NOTE:XBeta(0, 1) The following two hypotheses are being tested: 110 : e-2 vs Ha : ?-1. (a) Draw a graph of f(z | ?) when (i) Ho is true and when (ii) H. is true. Put both graphs on the same plot. Explain why a rejection region of the form (X<k) makes intuitive sense (b) Find k, so that the test has level a 0.05....
Problem 13.2 Assume that Xi, X2,. Xa form a random sample from a normal distribution for which the mean μ is unknown and the variance is 1 . Suppose the following are to be tested: H:H>0 hypotheses at the level of significance α,-0.025 and Let δ. denote the UMP test of these let π(u 18) denote the power function of the test procedure δ a) The yMP test rejects Ho when X 2 c. Determine the appropriate value for c...
Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test H0 : θ ≤ 1/3 vs H1 : θ > 1/3. a) Using the full sample, X1....Xn, find the form of the UMP test for the hypotheses H0: θ=1/3 vs H1: θ=1/2. b)If n=15 and α = 0.1, what is the rejection region and the size of test in (a)?
Let X1, . . . , Xn ∼ Geo(θ), f(x)= θ(1-θ)^x, and we wish to test H0 : θ ≤ 1/3 vs H1 : θ > 1/3. a) Using the full sample, X1....Xn, find the form of the UMP test for the hypotheses H0: θ=1/3 vs H1: θ=1/2. b)If n=15 and α = 0.1, what is the rejection region and the size of test in (a)?
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...
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For each of the following functions g determine if the corresponding functionf is continuous on the whole plane. Use "T" for true,"F" for false 2. g(x, y) 9x2y 3. gx, y)-4 sin) 4. g(x, y) xy sin(xy) 5. g(x, y) 3xy (1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For...
Consider the following pdf: ; 0<x<1 f(x)-2k ; l<x<2 0 otherwise (i)Determine the value of k. (ii) Find P(X 0.3) (iii) Find (0.1 〈 X 1.5).
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...
Problem 4 Define f(x) as follows θ2 -1<=x<0 1-θ2 0<=x>1 0 otherwise Let X1, … Xn be iid random variables with density f for some unknown θ (0,1), Let a be the number of Xi which are negatives and b be the number of Xi which are positive. Total number of samples n = a+b. Find he Maximum likelihood estimator of θ? Is it asymptotically normal in this sample? Find the asymptotic variance Consider the following hypotheses: H0: X is...
Define f(x) as follows θ2 -1<=x<0 1-θ2 0<=x>1 0 otherwise Let X1, … Xn be iid random variables with density f for some unknown θ (0,1), Let a be the number of Xi which are negatives and b be the number of Xi which are positive. Total number of samples n = a+b. Find he Maximum likelihood estimator of θ? Is it asymptotically normal in this sample? Find the asymptotic variance Consider the following hypotheses: H0: X...