andLetLet X ~ N(μ, E), whereΣμl = ==(:).LL2L121 1214121(X3 + X₁)r- (x²+x2)Y2X2=X3-X₁i) What is the distribution of Y?ii) Which components of Y are independent of each other?

Answered: Image /qna-images/answer/e0c8f7c5-39b9-4710-9646-b7e3c391957c.jpg

Answered: and Let Let X~ N(μ, E), where -- () Σ:…

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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Second part of c, as well as parts d and e
Suppose X, and X, have a bivariate normal distribution. Then, the condition distribution of X, given X, = x, follows a normal distribution with variance, o:(1-p)' of(1-p²) 0,(1-p²) a) b) c) d) 0,(1-p)
Please selct all that apply and explain why
A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?
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Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.
Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{O
Let X, and X2 be independent exponential distributions with the same parameter 2. What is the joint distribution of Y, = X, + X2 and Y, X1 -? What are the distributions of Y, and X1+X2 Y2?
Mln
Let X1,., Xn all be independent exponential distributions all with the same parameter 2. What is the distribution of the minimum of (X1,. a) what is the distribution of the smallest order statistic Y, ? b) Specify both the pdf of the distribution and describe the distribution and its parameters. ,Xn)? In other words:
please only answer part d, parts a,b,c have already been answered.
7 Let X1,...Xn be iid Normal( θ+ c, σ^2), where c and σ ^2 are known constants (i.e., E(Xi) = θ + c). Find a sufficient statistic forθ then obtain the minimum-variance unbiased estimator for θ.

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and Let Let X~ N(μ, E), where -- () Σ: = Y = 11214 121 12 14121 2 (X3+ X₁) 2X2 X3 - X₁ i) What is the distribution of Y? ii) Which components of Y are independent of each other?