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If X1, X2, X3 and X 4 are pairwise uncorrelated random variables, each having mean 0 and variance 16, compute the covariances and correlation coefficients of each of the following. (a) X1 X2 and X2 + X3: Cov(X1 X2, X2 + X3) = p(X1 + X2, X2 + X3) = (b) X1 X2 and X3 + X4: Cov(X1 X2, X3+X4) = 0 p(X1 + X2, X3 + X4) = 0

If X1, X2, X3 and X 4 are pairwise uncorrelated random variables, each having mean 0 and variance 16, compute the covariances and correlation coefficients of each of the following. (a) X1 X2 and X2 + X3: Cov(X1 X2, X2 + X3) = p(X1 + X2, X2 + X3) = (b) X1 X2 and X3 + X4: Cov(X1 X2, X3+X4) = 0 p(X1 + X2, X3 + X4) = 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 19E
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If X1, X2, X3 and X 4 are pairwise uncorrelated random variables, each having mean 0 and variance 16, compute the covariances and correlation coefficients of each of the following. (a) X1 X2 and X2 + X3: Cov(X1 X2, X2 + X3) = p(X1 + X2, X2 + X3) = (b) X1 X2 and X3 + X4: Cov(X1 X2, X3+X4) = 0 p(X1 + X2, X3 + X4) = 0
Transcribed Image Text:If X1, X2, X3 and X 4 are pairwise uncorrelated random variables, each having mean 0 and variance 16, compute the covariances and correlation coefficients of each of the following. (a) X1 X2 and X2 + X3: Cov(X1 X2, X2 + X3) = p(X1 + X2, X2 + X3) = (b) X1 X2 and X3 + X4: Cov(X1 X2, X3+X4) = 0 p(X1 + X2, X3 + X4) = 0
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