Question

In 2010 (with ~320 million people occupying 124.5 million homes nationwide), there were slightly more than 888,000 burgl...

In 2010 (with ~320 million people occupying 124.5 million homes nationwide), there were slightly more than 888,000 burglaries in a residence.

a. What is the probability your home will be broken into within the next year?

b. If your home is in a development of 100 homes, what number of break-ins can you expect in the next 20 years?

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Answer #1

a) The number of burglaries in a residence X can be assumed to be Poisson distributed with parameter (mean) 888,000 0.00713 124.5 x 106

The PMF of X is

P (X x) eIx 0,1,2,3, .... Here \lambda =0.00713 .

The probability of at least one burglary in a home next year is

P(X 1)= 1- P(X = 0) P(X 1) 1 -e0.00713 P(X 1) 0.0071

b) The number of burglaries per home per year is 0.00713. The number of burglaries per 100 homes per year is 0.00713 x 100 = 0.713

The number of break-ins in 20 years is 20 x 0.713 14,26

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