X-X~N(0,1), and W₁ =Y₁-HY~oyb) Let Z₁ =~N(0,1), for i=1,2,3,...,10, then:axi) State, with parameter(s), the probability distribution of the statistic, T =2Στις Wi54ii) Find the mean and variance of the statistic TW₁221, z* *iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4.iv) Find the value of such that P(T> B) = 0.01, where T = EZ² +².

Given Zi~N(0,1) and Wi~N(0,1) Result: t~F(a,b) Then Mean=E(t)=b/(b-2)…

Answered: b) Let Z₁ = X-X~N(0,1), and W₁…

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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Consider the following hypotheses: Ho: µ ≤ 201 HA: µ > 201 A sample is to be taken from a population with a mean of 203 and a standard deviation of 3. The hypothesis test is to be conducted using a significance level of 0.05. Determine the probability of committing a Type II error when n = 10 n = 20 n = 50
7. Let (z,.,) be a random sample from a normal distribution with mean ja and a variance at. Alo let S.. = , - z)* be the sum of squares of the randou sample. State without proof the sampling distribution of the following; (a) t(z) - ạ + b i-, 1,. n, as e positive eal constants. (- ) (b) t(z) - (E) (x) = (e) ti2) - (g) (r) = (e) t(2) = (d) t(a) Er, - E > ( - P (h) 시)- - -1 (-) (e) t(z)
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Please help me with this questions. thank you!
B) Let X1,X2, .,Xn be a random sample from a N(u, o2) population with both parameters unknown. Consider the two estimators S2 and ô? for o? where S2 is the sample variance, i.e. s2 =E,(X, – X)² and ở² = 'E".,(X1 – X)². [X = =E-, X, is the sample mean]. %3D n-1 Li%3D1 [Hint: a2 (п-1)52 -~x~-1 which has mean (n-1) and variance 2(n-1)] i) Show that S2 is unbiased for o2. Find variance of S2. ii) Find the bias of 62 and the variance of ô2. iii) Show that Mean Square Error (MSE) of ô2 is smaller than MSE of S?. iv) Show that both S2 and ô? are consistent estimators for o?.
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