Question: Suppose the length of time that it takes a laboratory rat to traverse a certain maze is a random variable, with density

\[f\left( x \right)=\left\{ \begin{aligned} & \frac{1}{16}x{{e}^{-x/4}}\,\,\,\,\text{if }x\ge 0 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{if }x<0 \\ \end{aligned} \right.\]

where x is measured in minutes

(a) Find the probability that a randomly selected rat will take no more than 5 minutes to traverse the maze

(b) Find the probability that a randomly selected rat will take at least 10 minutes to traverse the maze

(c) Find the expected value