Question

1. Let x = [−1,2,4,5]T, and let y = [2,1,−5,4]T. (a) Are x and y orthogonal?...

1. Let x = [−1,2,4,5]T, and let y = [2,1,−5,4]T. (a) Are x and y orthogonal? How can you tell? (b) Calculate x ̄ and y ̄. (c) Calculate the sample variance of y. (d) Calculate (sum){n, i=1, [(xi − x ̄) (yi − y ̄)].

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Answer #1

Q1 Let:

a) Two vector x and y are said to be orthogonal if x.y=0

therefore,

x.y=-1*2+2*1-4*5+5*4

=-2+2-20+20

=0

hence x and y are orthogonal.

b) The sample mean of x is given by

The sample mean of y is given by

c) The sample variance of y is given by:

The sample variance of y is s=3

d)

​​​​​​​

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