Let $ X $ be a three-dimensional normal vector with mean vector $\mu$ and covariance matrix $\Sigma$ given by:\[\mu = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix}\]\[\Sigma = \begin{pmatrix} 2 & 1 & 1 \\ 1 & 3 & -1 \\ 1 & -1 & 2 \end{pmatrix}\]Define the variables $ Y_1 $ and $ Y_2 $ as follows:- $ Y_1 = X_1 + X_2 + X_3 $- $ Y_2 = X_1 + X_3 $The task is to determine the conditional distribution of $ Y_1 $ given that $ Y_2 = 0 $.

Answered: 9. Let X be a three dimensional normal…

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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The distribution of certain test scores is a nonstandard normal distribution with a mean of 80 and a standard deviation of 9. What are the values of the mean and a standard deviation after all test scores have been standardized by converting them to z-scores using z=(x-µ)/σ? A) The mean is 100 and the standard deviation is 10 B) The mean is 0 and the standard deviation is 1 C) The mean is 1 and the standard deviation is 0 D) The mean is 10 and the standard deviation is 100
5
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3) Suppose test scores are measured by the Gaussian Normal Distribution N(X,75,10) calculate the following. a) Pr(80 < X < 90) b) Pr(50 < X < 70) c) The 95 th percentile
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Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 5.6 and standard deviation ? = 0.4. (d) Convert the z interval, z < −1.44, to an x interval. (Round your answer to one decimal place.) (e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.)

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9. Let X be a three dimensional normal with mean and covariance -(0) fl= 2 1 1 3 -1 2 == (1 Σ Set Y₁ = X₁ + X2 + X3 and Y2 = X1 + X3. Determine the conditional distribution of Y₁ given that Y₂ = 0