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# For 80% of lectures, Professor X arrives on time and starts lecturing with delay T=0. When Professor X is late, the starting time delay T is uniformly distributed between 0 and 300 seconds. Find the CDF and PDF of T.

Solution

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Observe that the lecturer starts on time with probability $0.8$. With probability $0.2$, there is a delay of the start which is uniformly distributed over $(0, 300)$.

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