Let X1,X2,X3 be random variables such that E(Xi) = μ and Var(Xi) = σ2 for all i. Find the value of the following quantities (as a function of μ and σ2) if the Xis are all mutually independent. Then repeat these calculations if each pair of variables have a correlation of ρ, that is, corr(Xi, Xj ) =ρ for i ≠ j. (a) E(X1 −X2 +X3) (b) Var(X1 − X2 + X3) (c) E(X21 − X22 + X23)

Let X1,X2,X3 be random variables such that E(Xi) = μ and Var(Xi) = σ2 for all i. Find the value of the following quantities (as a function of μ and σ2) if the Xis are all mutually independent. Then repeat these calculations if each pair of variables have a correlation of ρ, that is, corr(Xi, Xj ) =ρ for i ≠ j. (a) E(X1 −X2 +X3) (b) Var(X1 − X2 + X3) (c) E(X21 − X22 + X23)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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