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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 $=\frac{27 k}{4}=\frac{3}{2}$

Applications of Integration

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