If $x$ is uniformly distributed over (0, 15), the probability that $5 < x < 9$ is _____

\frac{1}{3}

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\frac{4}{15}

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\frac{2}{5}

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\frac{7}{15}

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Solution

The correct option is B $\frac{4}{15}$
$f (x) = \frac{1}{15 - 0} = \frac{1}{15}$
$P [5 < x < 9] = 9 \int 5 \frac{1}{15} d x = \frac{4}{15}$

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