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words,

(a) Show that is equivalent to

E

Σ=

Pearson.

o OXY

σYX o}

-μx

- HY

X-HX

Y-BY]]

(b) Is Σ symmetric?

(c) Let A be an arbitrary 2 by 2 matrix and b be an arbitrary two-dimensional vector. Let Z denote

X

a two-dimensional random vector defined as Z = A

+ b. What is the covariance matrix

of Z? Provide a detailed derivation.

(Hint: Note that the mean vector of Z is given by z = A

(1)

[^]

this question, the covariance matrix of Z can be obtained as E [(Z - µz)(Z - Hz)¹].)

+ b. According to part (a) of

Reference

[Oppenheim & Verghese] A. Oppenheim and G. Verghese, Signals, Systems, and Inference, 1st Ed.,

Fig: 1