Let the mean success rate of a Poisson process be 5 successe

Let the mean success rate of a Poisson process be 5 successes per hour. a. Find the expected number of successes in a 26 minutes period. (Round your final answer to the nearest whole number.) Expected number of successes b. Find the probability of at least 2 successes in a given 26 minutes period. (Round your answer to 4 decimal places.) Probability c. Find the expected number of successes in a one hour 48 minutes period. (Round your final answer to the nearest whole number.) Expected number of successes d. Find the probability of 8 successes in a given one hour 48 minutes period. (Round your answer to 4 decimal places.) Probability

Solution

(a) expected value= 26*5/60=2

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(b) Given X~Poisson(mean=2)

P(X=x)=(2^x)*exp(-2)/x!

So the probability is

P(X>=2) =1-P(X=0)-P(X=1)

=1-(2^0)*exp(-2)/1-(2^1)*exp(-2)/1

=0.5940

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(c) expected value= 108*5/60 =9

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(d) Given X~Poisson(mean=9 in one hour and 48 minutes)

P(X=x)=(9^x)*exp(-9)/x!

So the probability is

P(X=8) =(9^8)*exp(-9)/8! =0.1318