Suppose the random variables X1, X2,X, have the population variance/covariance matrix: -2 0 E=-2 5 0 0 1 1 Calculate the principal components and interpret their meaning. What can be gained from knowing these values?

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A: Solution

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A: The mean of X is given by:

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Q: (b) The variance-covariance matrix of three random variables X,, X, and X, is given by : 1 0.36 0.49…

A: the variance covariance matrix of three random variable    ∑ = 10.360.490.3610.250.490.251

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Q: Suppose the random variables X,,X2,X; have the population variance/covariance matrix: 1 -2 0 E=-2 0…

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Q: If X and Y are any random variables with COV(X, Y) = 0.25, o = 0.36, and o = 0.49, then the…

A: From the given information, Covx,y=0.25         σ2x=0.36         σ2y=0.49 Thus,

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Q: X A В X 3.56 -1.00 -2.89 -1.44 A -1.00 В -2.89 C -1.44 -0.07 0.47 3.16 3.38 2.13 -0.07 2.13 3.51…

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