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Homework 7.
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Homework must be answered in the order shown here (else please make a note telling the
reader where it is).
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Write your answers neatly
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Work must be shown for full credit
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No late homework accepted under any circumstances
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Staple the homework
1. Particles
independently arrive at a location at an average rate of five per minute. Let X be a
random variable modeling the number of particles arriving at the location in any 15minute
period and let Y be a random variable modeling the waiting time for the next arrival.
(a) What are reasonable random models for these variables?
Why?
(b) Using these models find the probability that there will arrive four particles in any particular
15minute period.
Show work.
(c ) Using these models find the probability that it takes between 4 and 6 minutes for the next
particle to arrive.
Show work.
2.A piece of equipment costing $10,000 has an exponentially distributed lifetime with an
average of 5 years. If the equipment fails during the first year, the manufacturer agrees to give a
full refund. If the equipment fails between the first and the second year, the manufacturer agrees
to give a halfprice refund. Finally, if the equipment fails after the second year but before the
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 Winter '09
 Work, Probability theory

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