alleryFor p.d.f. $f(x) = x/8$, $0 < x < 4$, the probability $P[x < 1.5]$ is:
A$0.5$
B$1/4$
C$0.28125$ (= $9/32$)
D$9/64$
Answer & Solution
Correct answer: D. $9/64$
$P[X < 1.5] = \int_0^{1.5} (x/8)\,dx = [x^2/16]_0^{1.5} = (1.5)^2/16 = 2.25/16 = 9/64 \approx 0.141$.
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