This is a very basic question but I was hoping you could all clarify.
If we have a probability density function $f(x)$ and we want to find, say $P(X = 1)$, we would find the area under the curve where $x = 1$, which is $0$.
However, if we consider the case of a Bernoulli distributed random variable where $P(X = 1)$ is $1/2$, and we know that the PDF of the Bernoulli distribution is $p^x(1-p)^{1-x}$, how would we possibly get the result that $P(X=1)$ is $1/2$ if we think in terms of the definite integral?