3. (15 points) It is Saturday morning and you want to watch the new season of Ga

Question

3. (15 points) It is Saturday morning and you want to watch the new season of Game of Thrones. You share a TV with your roommate but you have different preferences for shows, so you don't watch TV together. Your roommate woke up before you did and started watching The Stranger Things on Netflix at 10:00am. The amount of time it takes your roommate to finish watching Netflix is exponentially distributed with a mean of 40 minutes. You decide to make yourself breakfast and finish eating it at 10:45 am. If your roommate is still watching Netflix, you must wait for her to finish before you can watch your show. If the amount of time you spend watching TV is exponentially distributed with a mean of 60 minutes, at what time do you expect to finish watching TV?

Explanation / Answer

The mean of sum of n independent exponential distribution is the sum of their individual means

Here we have two independent exponential distribution with means 40 minuets and 60 minutes respectively

The mean of sum of two independent exponential variates is 60+ 40 = 100 minutes = 1 hour 40 minutes

The time at which second person is expected to finsh watching tv is 11.40 + 5 = 11.45

Note: extra 5 minutes is added for breakfast time

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