3) Let X1, X2, .., X, be i.i.d. N(@1,02). Show that the likelihood ratioprinciple for testing Ho : 02 = 6, specified, and 0, unspecified vs. H. : O2 #O2, 01 unspecified, leads to a test that rejects when%3D(T; – T)² < ¢1 or #; - 7)² > c2;i=1i=1where ci < c2 are selected appropriately.

Answered: Image /qna-images/answer/f411e84b-d0bb-43e7-bef6-839052eec1b3.jpg

Answered: 3) Let X1, X2,..., X, be i.i.d.…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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When the following hypotheses are being tested at a level of significance of a Ho: P2 100 H3: HZa O d. > Za/2
4.2.9. Let X₁, X2,..., X9 be a random sample of size 9 from a distribution that is N(μ, 0²). (a) Ifo is known, find the length of a 95% confidence interval for is based on the random variable √9(X -μ)/o. fl if this interval (b) Ifo is unknown, find the expected value of the length of a 95% confidence if this interval is based on the random variable √9(x-μ)/S. Hint: Write E(S) = (o/√n - 1)E[((n − 1)S²/0²)¹/2]. interval for fl (c) Compare these two answers.
If p value = 0.01, then ... (a,b,or c) a. the null is rejected at α = 0.1. b. the null will be rejected at both α = 0.1 and α = 0.05 c. the null is rejected at α = 0.05.
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7.2.3. X is the continuous uniform (-5, 5) random variable. Given the event B = {|X| < 3}, find the (a) conditional PDF, fx|B(x), (b) conditional expected value, E[X|B], (c) conditional variance, Var[X|B].
7.On average, what value is expected for the t statistic when the null hypothesis is true? а. О с. 1.96 b. 1 d. t>1.96
8. Given E(x,-)-78 and N= 80, then the population standard deviation, a, is approximately O a) 0.975 O b) 0.987 O0.994 Od) 0.110 SAMSUNG
Let Y₁, T₂, T3, T4, Is and X₁, Xe, Xq be Independent and normally From distributed random Sampits populations with mtans U₁ = 2 and 4₂ = 8 and Variances 0² = 5 and 0₂2₂²² = k respectively. Suppost P(x = √ > 10) = 0.02275, find the of 2 0₂²² = k· that Value
Suppose x is a normally distributed random variable with μ = 12 and o=2. Find each of the following probabilities. a. P(x214) b. P(x≤9) c. P(12.56 ≤x≤ 17.32) d. P(7.16 ≤x≤ 14.9) Click here to view a table of areas under the standardized normal curve. a. P(x ≥ 14) = (Round to three decimal places as needed.) ample Get more help. Table of Normal Curve Areas Z .00 wwwww BENER CREEP BEESE GEGEE 56045 AWNIO 0z Print 49960 49972 Done 60 I X
The random variable x has a normal distribution with mean 50 and variance 9. Find the value of x, call it x0, such that: a) P(x ≤ xo) = 0.8413 b) P(x > xo) = 0.025 c) P(x > xo) = 0.95 d) P(41 ≤ x ≤ xo) = 0.8630

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3) Let X1, X2,..., X, be i.i.d. N(01,02). Show that the likelihood ratio principle for testing Ho : 02 = 6, specified, and 0, unspecified vs. H. : 02 # 62, 01 unspecified, leads to a test that rejects when ("; – #)² < ¢1 or D(; – 1)² > c2, i=1