Y and Z are two random variables with Correlation of YZ of 0.5

IF X=2Z-1, then correlation of XZ is equal to;

Can anyone help? Thanks in advance (Happy)

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- Mar 6th 2011, 10:38 AMfirebrendCorrelation & linear regression
Y and Z are two random variables with Correlation of YZ of 0.5

IF X=2Z-1, then correlation of XZ is equal to;

Can anyone help? Thanks in advance (Happy) - Mar 7th 2011, 06:56 AMSambit
Correlation coefficient between X and Z = $\displaystyle \frac{Cov(X,Z)}{\sqrt{Var(X)}\sqrt{Var(Z)}}$ where

$\displaystyle Cov(X,Z) = Cov(2Z-1,Z) = 2Var(Z)$

and

$\displaystyle Var(X) = Var(2Z-1) = 4Var(Z)$

Now put these values in the first expression.

For further reasons behind this simplification, see Properties of Covariance and Properties of Variance

__Note__- By the way, your question is either incomplete or partially wrong since the answer has nothing to do with Correlation between Y and Z. Also, you need to know Var(Z).