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1. Let $X$ be a continuous random variable whose probability density function is $f(x)={4x_{3}?0?0?x?cotherwise?$ What is the value of $c$ that makes $f(x)$ a valid probability density function (PDF). 2. Let $f(x)={0.048x(5?x)0?0?x?5otherwise?$ (a) Verify that $f$ is a probability density function. (b) Find $P(X?4)$. 3. Sketch the region bounded by the given curves, and then find the area of the region. (a) $y=x_{2}?x,y=3?x_{2}$ (b) $y_{2}=x,4y?y_{2}=x$

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