Probability and Statistics

For a continuous random variable $X$ with probability density function $f(x)$, which condition must hold?

Options:

• (A) $\int_{-\infty}^\infty f(x) dx = 1$ and $f(x) \ge 0$
• (B) $f(x) \le 1$ always
• (C) $P(X = c) > 0$ for all real $c$
• (D) $\int_{-\infty}^\infty f(x) dx = 0$