$f(x) = 3x^2$ for $0 < x < 1$ is the p.d.f. of $X$. The probability $P[1/2 < X < 1]$ is:
A$3/8$
B$1/8$
C$1/2$
D$7/8$
Answer & Solution
Correct answer: D. $7/8$
$P[1/2 < X < 1] = \int_{1/2}^1 3x^2\,dx = [x^3]_{1/2}^1 = 1 - 1/8 = 7/8$.
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