統計學卜瓦松分配怎麼求?

2020-11-14 9:50 pm
請問(b)(c)怎麼解

回答 (1)

2020-11-15 12:47 am
✔ 最佳答案
X~Poi(2).
問:
(a) P[X = 5]
(b) P[X ≧ 5]
(c) P[X > 5]

P[X = 5] = 2^5e^(-2)/5! = 32e^(-2)/120 = (4/15)e^(-2)

P[X ≧ 5] = 1- P[X ≦ 4]
      = 1 - e^(-2){1+2+2^2/2+2^3/6+2^4/24}
      = 1 - 7e^(-2)

P[X > 5] = P[X ≧ 5] - P[X = 5]
      = 1 - 7e^(-2) - (4/15)e^(-2)
      = 1 - (109/15)e^(-2)


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