Deriving Distribution for Transformation

Setup

• Given $X$ as RV
• Given Probability Distribution $P(X\in B),\forall B\subset \mathbb{R}$
• Given Transformation $Y=h(X)$ that has a set of values $A$
• $P(Y\in A)=P(X\in h^{-1}[A])$

Techniques

• CDF Method Deriving Distribution for Transformation
• PDF Method Deriving Distribution for Transformation