匿名
匿名 發問於 科學及數學數學 · 1 十年前

Expected Value

On average, a machine breaks down 12 times in a year. Maintenance fee is free for the first 3 breakdowns and will charge $300 per breakdown if the number of breakdowns exceeds 3. If the number of breakdowns exceeds 10, a new machine will be bought. Given that no new machine is bought, find the expected maintenance cost to the nearest dollars. [Ans. $1614]

1 個解答

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  • ?
    Lv 7
    1 十年前
    最愛解答

    The no. of machine breaks down ~ Poi(12). Given that the information no new machine is bought => no. of break down <= 10

    So, the expected maintenance cost

    = [1/F(10)](300)[(12^4)e^(-12)/4! + 2(12^5)e^(-12)/5! + ... + 7(12^10)e^(-12)/10!]

    = (1/0.3472)(300)[0.0053 + 2(0.0127) + 3(0.0255) + 4(0.0437) + 5(0.0655) + 6(0.0874) + 7(0.1048)]

    = (1/0.3472)(300)(1.8675)

    = $1614

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