1)A random vector z = (x y) T has a joint probability density given by: a)Determine the correlation matrix of the z vector. b)Determine the covariance matrix of vector z. c)Determine if the v.a.s x and y are independent.

1)A random vector z = (x y) T has a joint probability density given by: a)Determine the correlation matrix of the z vector. b)Determine the covariance matrix of vector z. c)Determine if the v.a.s x and y are independent.

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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Question

1)A random vector z = (x y) ^Thas a joint probability density given by:
a)Determine the correlation matrix of the z vector.
b)Determine the covariance matrix of vector z.
c)Determine if the v.a.s x and y are independent.

Pzy(X,Y) = { C (a – X –
=
C(a-X-Y),
0≤x≤ a, 0≤Y ≤a - X
0, caso contrário.

Definition Definition Relationship between two independent variables. A correlation tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

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Step 1: Write the given information.

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Step 2: Determine normalisation constant C by integrating p(X, Y) over entire range and set it equal to 1.

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Step 3: Determine the value of Var(X).

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Step 4: Determine the variance(Y).

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Step 5: Determine the value of Cov(X,Y).

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Step 6: Determine the correlation matrix of the z vector.

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Step 7: Determine the covariance matrix of vector z.

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Step 8: Determine whether X and Y are independent.

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