1. (Poisson) Potholes on a highway can be a serious proble, and are in constant

Question

1. (Poisson) Potholes on a highway can be a serious proble, and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that there are, on the average, 2 potholes per mile after a certain amount of usage. It is assumed that the Poisson process applies to the random variable "number of potholes (a) What is the probability that two or more potholes will appear in a section of 1 mile? (b) What is the probability that no more than 4 potholes will occur in a given section of 5 miles? c) What is the mean number of potholes in 3 miles?

Explanation / Answer

Ans:

Poisson distribution:

a)On average there are 2 pathholes in one mile,so average rate=2 per mile

P(x>=2)=1-P(x<=1)

=1-e-2*(20/0!+21/1!)

=1-e-2*(1+2)=1-0.4060=0.594

b)On average there are 2 pathholes per miles,so average rate for 5 miles=2*5=10

P(x<=4)=e-10*(100/0!+101/1!+102/2!+103/3!+104/4!)

=e-10*(1+10+50+166.67+416.67)=0.0293

c)Average or mean number of pathholes of 3 miles=2*3=6 pathholes

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