Two bears are asleep in the cave that you are exploring. They will wake up at...

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Two bears are asleep in the cave that you are exploring. They will wake up at...

Two bears are asleep in the cave that you are exploring. They will wake up at at times T1 and T2, respectively (measured in minutes from the present moment, for example). Suppose that T1 and T2 are independent exponential random variables with rates λ1, and λ2 respectively. Let T be the first time at which one of the bear wakes up (i.e.T = min(T1, T2)). It would be wise to leave the cave before time T. (a) What is the distribution of T? (b) What is E(T)? (c) Answer the same questions in the case that there are n bears that wake up at independent T1, ...Tn, where Tk ∼ T xp(λk) and T = min(T1, T2, .., Tn).

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3. Two people, P1 and P2, stand in line to catch a taxi at an airport. P1 is first in the queue. The taxis arrive according to a Poisson process with parameter λC. P1 and P2 get tired of waiting for a...

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Two bears are asleep in the cave that you are exploring. They will wake up at...