Answered: Let X1,...,Xn be iid random variables…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 22E

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Question

Let X₁,...,X_n be iid random variables with expected value 0, variance 1, and covariance Cov [X_i,X_j] = ρ, for i≠j. Use Theorem of linearity of expectation to find the expected value and variance of the sum Y = X₁ +...+X_n.

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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