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[Solution] The following problem is a probability density function for a particular variable X. Use integration to find the indicated probabilities.

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

\[f(x)=\left\{ \begin{aligned} & \frac{1}{8}(4-x)\text{ if }0\le x\le 4 \\ & 0\text{ otherwise} \\ \end{aligned} \right.\]
  1. \(\Pr (0\le X\le 4)\)
  2. \(\Pr (2\le X\le 3)\)
  3. \(\Pr (X\ge 1)\)

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