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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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)
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).
