8.3.16. Let (X₁,Y₁), (X2, Y2),..., (Xn, Yn) be a random sample from a bivariatenormal distribution with #1, #2, 0 = 0 = 0², p=, where 1, 2, and o2 > 0 areunknown real numbers. Find the likelihood ratio A for testing Ho: 1 = 2 = 0,0²unknown against all alternatives. The likelihood ratio A is a function of whatstatistic that has a well-known distribution?

Given: Let X1, Y1, X2, Y2,......,Xn, Yn be a random sample from a bivariate normal distribution with…

Answered: 28.3.16. Let (X₁, Y₁), (X2, Y2),...,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. Let Y₁, Y₂, Y3, Y4, Y5 and X₁, X₂, ..., X, be independent and normally distributed random samples from populations with means μ₁ = 2 and μ₂ = 8 and variances ₁² = 5 and ₂² = k₁ respectively. Suppose that P(X-Ỹ > 10) = 0.02275, find the value of 0₂² = k. (5) Suppose that Y. Y y and X. X. X are independent normally distributed random
Let X. X , be a random sample of siren from a normal distribution with population mean 0 and population variance a>Ois unknown, that is N(0, ). Suppose that we define the following plvotal quantity (n-1)s where & and S' are the sample mean and the sample variance, respectively. Use the plvotal quantity (Q) to derive the (1- a) 100% confidence interval (C) for the unknown parameter (o) if the two critical values are q--n, a) and (n-1) (A) CI = (n8+(n-1)51 + n-1) s (8) CI - (C) CI - + (n-1) s (D) CI= O D O A O c O B
Suppose X₁,, Xn from a normal distribution N(μ, o²) where both μ and o are unknown. We wish to test the hypotheses Ho: o² = o vs. Ha: 0² # of at the level a. Show that the likelihood ratio test is equivalent to the x² test.
Suppose that Y₁, Y₂, ..., Ym is a random sample of size m from Gamma (a = 3, B = 0), where 0 is not known. Check whether or not the maximum likelihood estimator Ô is a minimum variance unbiased estimator of the parameter 8.
Q2: Let x1,X2, . , Xn and y1, y2, ..., Ym represent two independent random samples from the respective normal distributions N(H1,07) and N (H2, 03). It is given that of = 30, but ožis unknown. Then 1. A random variable that can be used to find a 95% confidence interval for - is (x- y) - (H1 - H2) А. ns3 + ms n+m. 3(n+m-2)"tm, nm O A (x – y) – (41 – H2) В. ns? + ms; n + m. (n + m – - 2) пт (x – y) – (41 - H2) С. ns3 + mS;_n+3 3(n+ m-2) ("+3m nm Ос
We have the following information about the random variables X and Y: |x = 1, |y = −1.5 , ox = 0.25, c} = 1. o Calculate the variance of Z = 3X + 5Y, a) when the coefficient of correlation is p(X, Y) = 0.46: 0²77 34.15 Z b) when X and Y are independent random variables: 0²2 27.75 X
2
5. Let (Xi, Yi), i 1, 2, ,n, be a random sample from a bivariate normal distribution. Find the joint distribution of (X,Y).
2.STATISTICAL INFERENCE
just please answer the sub-b
Assume that X and Y are random variables with the following parameters: 4 аnd o'y 13, 12, о Hy What is the variance of Z if Z = 2X - Y + 1 and ory =0.8

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