Poisson Distribution | poisson distribution lambda
ItisoftenacceptabletoestimateBinomialorPoissondistributionsthathavelargeaverages(typically≥8)byusingtheNormaldistribution.SincetheBinomialandPoissonarediscreteandtheNormaliscontinuous,itisnecessarytousewhatitcalledthecontinuitycorrectiontoconvertthecontinuousNormalintoadiscretedistribution.Thisisaccomplishedbycomputingtheprobability(area)foreachdiscretevalueofxbycomputingtheprobabilitythattherandomvariableXisbetweenx±0.5.f(X=x)=P(x−0.5≤X≤x+0.5) =P(X≤x+0.5)−P(X≤x−0.5) =F(x+0.5)−F(x−0.5)=Φ...
It is often acceptable to estimate Binomial or Poisson distributions that have large averages (typically ≥ 8) by using the Normal distribution. Since the Binomial and Poisson are discrete and the Normal is continuous, it is necessary to use what it called the continuity correction to convert the continuous Normal into a discrete distribution. This is accomplished by computing the probability (area) for each discrete value of x by computing the probability that the random variable X is between x ± 0.5.
f(X=x)=P(x−0.5≤X≤x+0.5) =P(X≤x+0.5)−P(X≤x−0.5) =F(x+0.5)−F(x−0.5)=Φ(Zx+0.5)−Φ(Zx−0.5)
Example 7.7Discrete normal probability approximation of Binomial and Poisson distributions
A delivery service has a fleet of 60 trucks. Each day, the probability of a truck being out of use due to factors such as breakdowns or maintenance is 10%.
a.What is the probability that s...