X is a 3-dimensional random vector with ex 0 and, Basic Statistics

X is a 3-dimensional random vector with ex 0 and

X is a 3-dimensional random vector with E[X] = 0 and autocorrelation matrix R_X with elements

Y is a 2-dimensional random vector with

Use Y to form a linear estimate of X₁:

(a) What are the optimum coefficients and ₂?

(b) What is the minimum mean square error e∗ L?

(c) Use Y1 to form a linear estimate of X₁: ₁ = aY₁ + b. What are the optimum coefficients a∗ and b∗? What is the minimum mean square error e∗_L?

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Basic Statistics: X is a 3-dimensional random vector with ex 0 and

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Basic Statistics: X is a 3-dimensional random vector with ex 0 and

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