Continuous Random Variable

Definition

Let

• $X$ : Random variable
• $F(x)$ : cdf of $X$

If $F(x)$ is continuous for all $x\in \mathbb{R}$

Then we say $X$ is a continuous random variable

Properties

If $X$ is continuous, then $P(X=x)=0,\forall x\in \mathbb{R}$.

Related theorems

• Theorem 1.7.1 Finding the pdf of a transformation