The Chozo brand surge protector tolerates three voltage spik

The Chozo brand surge protector tolerates three voltage spikes and dies on the fourth spike. Assume that voltage spikes may be modeled by a Poisson process with an average rate of 3.5 spikes per year.

a. Compute the expected lifetime of the surge protector.

b. Compute the probability the surge protector will last more than 2 years.

Solution

A)

Expected lifetime = 4 spike / (3.5 spikes/year) = 1.142857143 years [ANSWER]

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b)

There is an average of 2*3.5 = 7 spikes in 2 years.

This question is like asking at most 3 spikes happen in 2 years.

Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    7      
          
x = the maximum number of successes =    3      
          
Then the cumulative probability is          
          
P(at most   3   ) =    0.081765416 [ANSWER]