優(yōu)化營(yíng)銷(xiāo)平臺(tái)流程-資料下載頁(yè)
2025-01-22 13:31本頁(yè)面
【正文】 Code As with the Binomial distribution, the codes dpois and ppois will do the calculations for you. x=dpois(0:20,) x [1] [6] [11] [16] [21] barplot(x,names=0:20) Now check that ppois gives the same answer (ppois is a cumulative distribution). ppois(2,) [1] Consider a collection of graphs for different values of ? ?=3 ?=4 ?=5 ?=6 ?=10 In the last case, the probability of 20 arrivals is no longer negligible, so values up to, say, 30 would have to be considered. Properties of Poisson The mean and variance are both equal to ?. The sum of independent Poisson variables is a further Poisson variable with mean equal to the sum of the individual means. As well as cropping up in the situations already mentioned, the Poisson distribution provides an approximation for the Binomial distribution. Approximation: If n is large and p is small, then the Binomial distribution with parameters n and p, ( B(n。p) ), is well approximated by the Poisson distribution with parameter np, . by the Poisson distribution with the same mean Example Binomial situation, n= 100, p= Calculate the probability of fewer than 10 successes. pbinom(9,100,) [1] This would have been very tricky with manual calculation as the factorials are very large and the probabilities very small The Poisson approximation to the Binomial states that ? will be equal to np, . 100 x so ?= ppois(9,) [1] So it is correct to 2 decimal places. Manually, this would have been much simpler to do than the Binomial. 演講完畢，謝謝觀看！
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