Linear Function of a Discrete Random Variable
\[Y=aX+b\] \[p_Y(y)=p_X\!\left(\frac{y-b}{a}\right)\]Linear Function of a Continuous Random Variable
\[Y=aX+b\] \[f_Y(y)=\dfrac{1}{\lvert a\rvert}f_X\!\left(\frac{y-b}{a}\right)\]General Function \(g(X)\) of a Continuous Random Variable
Two steps:
- Find the CDF of \(Y\)
- Differentiate