卜氏分佈是二項次的極限分配-排列組合機率53

 

假設注射某疫苗的人有不良反應的機率為 0.001，求 2,000 人中
(1) 恰有 3 人 ， (2) 超過 2 人 注射後有不良反應的機率。
因為：n = 2,000， p = 0.001 期望值(平均值)E(X)=λ=np= 2,000 ×0.001 = 2
(1) P ( x = 3 ) = (2^3e^-2)/3!  = 0.180
(2) P ( x> 2) = 1 – {P ( x = 0 ) +P ( x = 1 ) +P ( x = 2 )} = 1 – ( 0.135 + 0.271 +
0.271) =1-0.677=0.323

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抽樣數	不良率	發生次	期望值E(X) =λ=np	=POISSON (k,λ,0)	=POISSON (k,λ,1)
n	p	k	λ	=POISSON (C4,D4,0)	=1-POISSON (C4,D4,1)
2000	0.001	0	2	13.5335%	86.4665%
2000	0.001	1	2	27.0671%	59.3994%
2000	0.001	2	2	27.0671%	32.3324%
2000	0.001	3	2	18.0447%	14.2877%
2000	0.001	4	2	9.0224%	5.2653%
2000	0.001	5	2	3.6089%	1.6564%
2000	0.001	6	2	1.2030%	0.4534%
2000	0.001	7	2	0.3437%	0.1097%
2000	0.001	8	2	0.0859%	0.0237%
2000	0.001	9	2	0.0191%	0.0046%
2000	0.001	10	2	0.0038%	0.0008%