Kidney transplant in 2012 have interarrival times that are independe.pdf

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Kidney transplant in 2012 have interarrival times that are independent with a common distribution that is exponential with mean 3 per month. Calculate the probability that at least three kidney transplant claims will arrive between January 1, 2012 and March 1, 2012 Solution So nos. of transplants will follow Poisson distribution =rate*time=3*2=6 P(x=k)= e-k/k! P(X>=3) = 1-P(X<3) = 1-P(x=0)-P(x=1)-P(x=2)= 1- e-6- 6*e-6-18*e-6= 0.938.

Kidney transplant in 2012 have interarrival times that are independent with a common
distribution that is exponential with mean 3 per month. Calculate the probability that at least
three kidney transplant claims will arrive between January 1, 2012 and March 1, 2012
Solution
So nos. of transplants will follow Poisson distribution
=rate*time=3*2=6
P(x=k)= e-k/k!
P(X>=3) = 1-P(X<3) = 1-P(x=0)-P(x=1)-P(x=2)= 1- e-6- 6*e-6-18*e-6= 0.938

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