Question: Waiting Time Suppose that a traffic light on your campus remains red for 30 seconds at a time. You arrive at that light and find it red. Assume that your waiting time \(t\) (in seconds) at the light follows a uniform density function \(y=u(t)\).

1. Why does it make sense that \(u(t)=0\) for \(t<0\) and \(t>30 ?\)
2. Sketch a graph of \(u\).
3. Find your chances of waiting at least 10 seconds at the red light. What does this value represent on the graph of \(u\) ?
4. Find the probability of waiting no more than 20 seconds at the red light.
5. What is the average time you would expect to wait at the light?

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