ㄚ生 asked in 科學數學 · 6 years ago

求解統計學題目!~急(20點奉上)

1.設有兩獨立隨機變數X.Y :令W=X+Y,請依照以下不同的分配求算:

(1)E(W): (2)Var(W): (3)P(W=5): (4)E(W+3): (5)Var(2W+3)

(a)X~B(10,0.4) ,Y~B(20,0.4)

(b)X~N(15,3),Y~N(10,7)

2.假設證券交易所中,客戶等候交割時間呈指數分配,平均需時25分。試求某位客戶必須等20至30分鐘完成交割的機率。

1 Answer

Rating
  • 才銘
    Lv 5
    6 years ago
    Favorite Answer

    1.

    (a) W=X+Y~B(30,0.4)

    (1) 30×0.4=12

    (2) 30(0.4)(1−0.4)=7.2

    (3) C(30,5)(0.4^5)[(1−0.4)^25]≒0.0041

    (4) E(W+3)=E(W)+3=15

    (5) Var(2W+3)=4Var(W)=28.8

    (b) W=X+Y~N(25,10)

    (1) 25

    (2) 10

    (3) 0

    (4) 25+3=28

    (5) 4×10=40

    2. λ=1/25

    →P(20<30)

    =P(X<30)−P(X<20)

    =[1−e^(−30/25)]−[1−e^(−20/25)]

    ≒0.1481<30)

    2015-04-11 21:55:04 補充:

    →P(20<30)

    =P(X<30)−P(X<20)

    =[1−e^(−30/25)]−[1−e^(−20/25)]

    ≒0.1481

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