The p.d.f. of \(X\) is \(f(x)=kx^2\) for \(0\le x\le3\) and 0 otherwise. Then \(P(X\le1)\) is
A. \(\frac19\)
B. \(\frac13\)
C. \(\frac1{27}\)
D. \(\frac8{27}\)
1 answer
Best answer
Answer: C. \(\frac1{27}\)
\(\int_0^3kx^2dx=9k=1\Rightarrow k=\frac19\); \(P(X\le1)=\frac19\cdot\frac13=\frac1{27}\).
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· 23 Oct 2026
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