= Solution
In the <probability density function> convention used here, a <random variable> $X$ has a nonnegative <probability density function> $f$, with $\int_{\mathbb R}f(x)\,\mathrm dx=1$, such that for every <Borel set> $A$,
$$
\boxed{\mathbb P(X\in A)=\int_A f(x)\,\mathrm dx.}
$$
In particular, its <cumulative distribution function> is $F(x)=\int_{-\infty}^x f(t)\,\mathrm dt$ and individual points have <probability> zero. More precisely, this property is the statement that the distribution is an <absolutely continuous probability distribution>; <continuity> of the <cumulative distribution function> alone is a weaker property and need not imply a <probability density function>.
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