Question

For a probability density function (pdf), the probability of a single point is

• A. $1$
• B. $2$
• C. $0$
• D. Constant

Answer 1

The correct option is C $0$

We know that the probability density functions are defined for an infinite number of points over a continuous interval, the probability at a single point is always zero. Probabilities are measured over intervals, not single points. That is, the area under the curve between two distinct points defines the probability for that interval.

For a continuous random variable $X$, we will always have $P(X=x)=0$, since the area under a single point of a curve is always zero.

In other words, if $X$ is a continuous random variable, the probability that $X$ is equal to a particular value will always be zero.

Hence for a probability density function (pdf), the probability of a single point is $0$.