Home › Agniveer Navy › Mathematics › Binomial Theorem › For a **probability density function (p.d.f.)** …
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.
Related questions
In the expansion of a bracket raised to four, the sum of indices is:How many terms are in the expansion of a bracket raised to twelve?How many terms are in the expansion of a bracket raised to five?In the last term of the expansion, the index of b is:In the first term of the expansion, the index of b is:In the first term of the expansion, the index of a is:The general rule for expansion is built using the concept of:Why is Pascal's triangle awkward for a large index?