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Light Bulbs A red light bulb has been flashing forever, according to a Poisson process with rate...

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Basic Math

Light Bulbs

A red light bulb has been flashing forever, according to aPoisson process with rate r. Similarly, a blue bulb has beenflashing forever, according to an independent Poisson process withrate b. Let us fix t to be 12 o'clock.

1 What is the expected length of the interval that t belongs to?That is, find the expected length of the interval from the lastevent before t until the first event after t. Here, an event refersto either bulb flashing.

2 What is the probability that t belongs to an RR interval?(That is, the first event before, as well as the first event aftertime t, are both red flashes.)

3 What is the probability that between t and t+1, we haveexactly two events: a red flash followed by a blue flash?

Answer & Explanation Solved by verified expert
3.9 Ratings (514 Votes)
A red light bulb X has been flashing forever according to aPoisson process with rate rA blue bulb Y has been flashing forever according to anindependent Poisson process with rate bSince Red    See Answer
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