Question

A continuous random variable $X$ has p.d.f $f\left(x\right)$, then:

• A. $0\le f\left(x\right)\le 1$
• B. $f\left(x\right)\ge 0$
• C. $f\left(x\right)\le 1$
• D. $0<f\left(x\right)<1$

Answer 1

The correct option is B $f\left(x\right)\ge 0$

Let $X$ be a continuous random variable.

Let $f\left(x\right)$ be the p.d.f of $X$.

We know that the p.d.f $f\left(x\right)$ of a continuous random variable $X$ is always positive. That is $f\left(x\right)\ge 0,\forall x\in R$

Thus a continuous random variable $X$ has p.d.f $f\left(x\right)$ then $f\left(x\right)\ge 0$