Consider the random vector y with the following population mean vector and population correlation matrix P...
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Consider the random vector y with the following population mean vector and population correlation matrix P y = Y/1 3/2 (0) H = X1 = 43 22 65 58 The population variances of the variable in y are: Additionally, define the the following subvectors: x₂ = (1/h) y/₁ y4 P₁ = 1.00 0.80 0.50 -0.40 0.80 1.00 0.75 -0.30 0.50 0.75 1.00 -0.35 -0.40 -0.30 -0.35 1.00 ₁1 = 25, 022=16, 033 = 64, and 44 = 100. X3 = y/₁ Y3 y4 a. Determine the covariance matrix (E) of y. b. Determine the distribution of the difference in the sum of the first two variables (y₁ and 32) and the sum of the last two variables (ya and y₁). NOTE: This is the distribution of a single random variable. c. Determine the joint distribution of the three following random variables. W₁ = 4y₁-3y2 + 2y3 - Y4 20¹2 = ₁ + 2y2+2y+3y4 - 10 wx = 5yı -4ys +2 d. Are any pairs of variables among the three random variables in part c. independent? Justify your answer. e. Determine the distribution of y2. f. Determine the distribution of x₁. g. Determine a matrix A and a vector b such A(x₁ - b) ~ x²- h. Determine the distribution of x1|x2. i. Determine the distribution of x3y2. Consider the random vector y with the following population mean vector and population correlation matrix P y = Y/1 3/2 (0) H = X1 = 43 22 65 58 The population variances of the variable in y are: Additionally, define the the following subvectors: x₂ = (1/h) y/₁ y4 P₁ = 1.00 0.80 0.50 -0.40 0.80 1.00 0.75 -0.30 0.50 0.75 1.00 -0.35 -0.40 -0.30 -0.35 1.00 ₁1 = 25, 022=16, 033 = 64, and 44 = 100. X3 = y/₁ Y3 y4 a. Determine the covariance matrix (E) of y. b. Determine the distribution of the difference in the sum of the first two variables (y₁ and 32) and the sum of the last two variables (ya and y₁). NOTE: This is the distribution of a single random variable. c. Determine the joint distribution of the three following random variables. W₁ = 4y₁-3y2 + 2y3 - Y4 20¹2 = ₁ + 2y2+2y+3y4 - 10 wx = 5yı -4ys +2 d. Are any pairs of variables among the three random variables in part c. independent? Justify your answer. e. Determine the distribution of y2. f. Determine the distribution of x₁. g. Determine a matrix A and a vector b such A(x₁ - b) ~ x²- h. Determine the distribution of x1|x2. i. Determine the distribution of x3y2.
Expert Answer:
Answer rating: 100% (QA)
a To determine the covariance matrix of y we can use the formula diag P Using the given values 25 0 0 0 0 16 0 0 0 0 64 0 0 0 0 100 1 08 05 04 08 1 07... View the full answer
Related Book For
An Introduction To Statistical Methods And Data Analysis
ISBN: 9781305465527
7th Edition
Authors: R. Lyman Ott, Micheal T. Longnecker
Posted Date:
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