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Correlation of X with X plus Y

EasyStatistics~3m

Random variables have Var⁡(X)=4\operatorname{Var}(X)=4, Var⁡(Y)=9\operatorname{Var}(Y)=9, and Cov⁡(X,Y)=3\operatorname{Cov}(X,Y)=3. What is the correlation between XX and X+YX+Y? Give a decimal to four places.

Show hints (2)+
  1. Cov⁡(X,X+Y)=Var⁡(X)+Cov⁡(X,Y)\operatorname{Cov}(X,X+Y) = \operatorname{Var}(X) + \operatorname{Cov}(X,Y).
  2. Var⁡(X+Y)\operatorname{Var}(X+Y) needs the 2Cov⁡(X,Y)2\operatorname{Cov}(X,Y) cross term; then divide by Var⁡(X)Var⁡(X+Y)\sqrt{\operatorname{Var}(X)\operatorname{Var}(X+Y)}.

Answer

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0.803 (± 0.001)

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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