Calculus: Other Calculus Problems – #454


Question: The following problem is a probability density function for a particular variable \(X\). Use integration to find the indicated probabilities.

\[f(x)=\left\{ \begin{align}
& \frac{1}{8}(4-x)\text{ if }0\le x\le 4 \\
& 0\text{ otherwise} \\
\end{align} \right.\]

(a) \(\Pr (0\le X\le 4)\)

(b) \(\Pr (2\le X\le 3)\)

(c) \(\Pr (X\ge 1)\)

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