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# Let $f(x) = k(3x - x^2)$ if $0 \le x \le 3$ and $f(x) = 0$ if $x < 0$ or $x > 3$.(a) For what value of $k$ is $f$ a probability density function?(b) For that value of $k$, find $P (X > 1)$.(c) Find the mean.

## A. $k=\frac{2}{9}$B. $P(X > 1)=\frac{20}{27}$C. Mean $=\frac{27 k}{4}=\frac{3}{2}$

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Applications of Integration

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Applications of Integration

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