Qr. Let the pdf of X be f (x|0) = Ox®-!I(0 < x < 1) for 0 = 1,2. To test the simple hypothesis %3D Ho : 0 = 1 against the alternative simple hypothesis H1 : 0 = 2, we use a random sample X1, X2 of size 2 and define the critical region C = {(x1,12) : 0.75 < 1172}. (a) Find the power function of the test. (b) If the realized test statistic 11 and I2 are o.8 and o.9, do we reject the Ho?

Qr. Let the pdf of X be f (x|0) = Ox®-!I(0 < x < 1) for 0 = 1,2. To test the simple hypothesis %3D Ho : 0 = 1 against the alternative simple hypothesis H1 : 0 = 2, we use a random sample X1, X2 of size 2 and define the critical region C = {(x1,12) : 0.75 < 1172}. (a) Find the power function of the test. (b) If the realized test statistic 11 and I2 are o.8 and o.9, do we reject the Ho?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Suppose Xn is the sample mean of a random sample of size n from a distribution that has a Gamma(2,1/2) (where a = 2, B = }) pdf f(x) = 4xe-2a, 0 < x < ∞, zero elsewhere. Use the Central Limit Theorem to deduce that the random variables Vn(Xn – 1) converges in distribution to N(0, 1/2).
Prob ... solve Q 5 & Q 6
Let X1, . . . , Xn ∼ iid Unif(0, θ). (a) Derive an asymptotic distribution for the MOM estimator ˜θ = 2X¯ of the form.(b) From this choose an approximate pivot and interval to get an interval that asymptotically has100(1 − α)% coverage.
Let s be the sample variance of a random sample of size n1 fron a Normal(41,o²) population and s, be the sample variance of a random sample of size 12 from a Nornal(µ2,0²) population and the two samples are independent. Note that the two samples have the same population variance o² but µi # j12 and n1 # 12. Define the pooled variance estimator as (n1 – 1)sỉ + (n12 – 1)s3 T1 + n2 - 2 -- Is s? unbiased for o2 ? Explain with precisc computation. Find the distribution of ºP. Give the reasoning of your answer. Find the variance of s.
where alpha > 0, find the method of moments (MOM) estimator for alpha.
2.21 Let the random variable X have pdf { f(x) = = 49 X - 3 0 < x < 1, 1 < x < 2. Generate a random variable from f(x), using a) the inverse-transform method, b) the acceptance-rejection method, using the proposal density g(x) = 1/2/₁ 0 ≤ x ≤ 2.
Derive the following:(c) variance(d) moment generating function
Let X1,..., Xn be iid pdf JKa,cx-a-1, f (x) = 0, x > c, x < c. and unknown parameters a and c. (a) Determine Ka.c. (b) Find the maximum likelihood estimator of c. (c) Find the maximum likelihood estimator of a. If you decide to use calculus methods, you have to do a second derivative test.
Consider the bivariate Gaussian distribution 1 p(x1, x₂) = N( X2) = N([1₂] ₁ 69. 2 (a) Compute the marginal distribution for each dimension. (b) Compute p(x₁|x2 = 1) and p(2x1, 3x2).
Q. 3 Let continuous random variables X and Y be independent identically distributed random variables with the following respective pdfs: fx(x) = 2e-2x;x 2 0 and fy (y) = 2e-2y;y > 0 Define a new random variable Z = X + Y. Derive moment generating function of Z, i.e. Mz(t).
page 328 5.2.2
If X1, X2,...,Xn is a random sample from a distribution having pdf of the form f(x; 0) = 0x°-1, 0 < x < 1, zero elsewhere, show that a best critical region for testing Ho : 0 = 1 against H1 : 0 = 2 is C = {(x1, 12, ..., Tn) : c< II-1 *i}. ----- DA --