The probability that a continuous random variable falls inside an interval $[c, d]$ corresponds to:
AThe height of $f$ at $c$
BThe slope of $f$ between $c$ and $d$
CThe area under $f(x)$ between $x = c$ and $x = d$
D$d - c$ always
Answer & Solution
Correct answer: C. The area under $f(x)$ between $x = c$ and $x = d$
$P[c < X < d] = \int_c^d f(x)\,dx$ — the area under the p.d.f. curve between $c$ and $d$. Total area over the support = 1.
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