# 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) $$\Pr (X\ge 1)$$