# 統計~有關Poisson distribution 跪求神人幫忙解題><?

The number of automobiles that arrive at a certain intersection per minute has a Poisson distribution with a mean of 5. Interest centers around the time that elapses before 10 automobiles appear at the intersection.

(a) What is the probability that more than 10 automobiles appear at the intersection during any given minute of time?

(b) What is the probability that more than 2 minutes elapse before 10 cars arrive?

### 1 個解答

• 最佳解答

Poisson's distribution applies to the above situation where the average (μ=5 per minute), and the probability that exactly x occurrences happen in a particular minute has a probability of

P(x; μ) = e^(-μ) (μ^x) / x!

Given μ=5.

(a)

P(10;5)=e^(-5)*(5^10)/10!=0.01813

(b)

Using a period of 2 minutes, μ=2*5=10.

Probability of up to 9 cars arrive is given by summing P(X<10)=P(x;10) for x=0,1,....9

P(X<10)=5.54*10^-5+4.54*10^-4+0.00227+0.00757+...+0.1126+0.1251=0.45793

For more explanations and examples, see reference link.