Which of the following is/are NOT correct about a continuous random variable? CHECK ALL THAT APPLY.

A. It can only take on integer values.
B. The probability that it has a value that falls between real values $a$ and $b$ is given by the area under the density function over the range $(a,b).$
C. The probability that it has a value equal to $x$ is given by $f(x)$ where $f$ is the density function.