For a **probability density function (p.d.f.)** $f(x)$ of a continuous random variable over support $S$, the two conditions are:
A$f(x) \leq 0$ everywhere
B$f(x) \geq 0$ on $S$ and $\int_S f(x)\,dx = 1$
C$f(x) > 1$ on $S$
D$f(x) \geq 0$ and $\sum f(x) = 1$
Answer & Solution
Correct answer: B. $f(x) \geq 0$ on $S$ and $\int_S f(x)\,dx = 1$
p.d.f. conditions: (i) $f(x) \geq 0$ everywhere on the support; (ii) total area under the curve = 1, i.e. $\int_S f\,dx = 1$. Note that $f(x)$ itself can exceed 1 — it's a density, not a probability.
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