Correlation & 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)

Correlation coefficient between X and Z = where

and


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).