Question

- At a 24-hour computer repair facility broken-down computers
arrive at an average rate of 3 per day, Poisson distributed.
- What is the probability that on a given day no computers arrive for repair?
- What is the probability that on a given day at least 3 computers arrive for repair?
- What is the distribution of the time between arrivals of computers to this facility and what is the average time between arrivals?
- On one particular day no computer has arrived for repair until
noon. What is your best estimate of when the next computer will
arrive for repair? Hint:
*forgetfulness*property of the exponential distribution*.* - Suppose a computer has just arrived for repair. What is the probability that the next one will not arrive for at least another 5 hours?

Answer #1

a) probability that on a given day no computers arrive for
repair =e^{-3}*3^{0}/0! =0.0498

b) probability that on a given day at least 3 computers arrive for repair =P(X>=3) =1-P(X<=2)

=1-(P(X=0)+P(X=1)+P(X=2))
=1-(e^{-3}*3^{0}/0!+e^{-3}*3^{1}/1!+e^{-3}*3^{2}/2!)
=0.8647

c)

distribution of the time between arrivals of computers to this facility is exponential with mean time between arrival =1/3 days

or (24/3) =8 hours

d)

best estimate for next computer will arrive for repair =* hour after noon or at 8.00 pm

e)

probability that the next one will not arrive for at least
another 5 hours =P(T>5)=e^{-5/8} =0.5353

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