(a) If F(x) is the cumulative distribution of the probability density function f(x), explain why F(a) is the area under f(x) to the left of a.
(b) If F(x) is the cumulative distribution of the probability density function f(x), what is the limiting value of F(x) as x increases without bound?
Suppose
\[ \begin{align}
p(x) &= \frac{1}{20} \quad \text{for} \quad 0 \le x \le 20
\end{align} \ \]
is a probability density function.
(a) Without using calculus, find P(x < 2) and P(x > 5).
(b) Without using calculus, find P(3 < x < 12).