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Math Help - propability

  1. #1
    Newbie
    Joined
    Apr 2008
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    3

    Unhappy propability

    Hi guys,

    Im new to the forum and this is my first post. I am in very urgent need of some help I have been practising some prob & stat for an exam, tomorrow and have been doing pretty well till I came upon this question. Can anyone help I dont understand this topic very well and I have reason to believe that a similar question will come on the exam tomorrow I want to know how to go about doing it thanks in advance.

    Alicia

    The question is attached. Thanks a million.
    Attached Thumbnails Attached Thumbnails propability-prob-stats-question.jpg  
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  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
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    802
    Hello

    (a) The probability that the profit is lower than u is P(X\leq u)=\int_{-\infty}^uf(x)\,\mathrm{d}x. If you want to know the probability that the profit is between u and v ( u<v), you'll have to evaluate the probability that it is lower than v and greater than u : it boils down to calculating P(X\leq v)-P(X\leq u) = \int_{-\infty}^vf(x)\,\mathrm{d}x-<br />
\int_{-\infty}^uf(x)\,\mathrm{d}x = \int_u^vf(x)\,\mathrm{d}x because if the profit is lower than v it is necessarily lower than u.

    (b) The expected value of the profit is given by \int_{-\infty}^{\infty}xf(x)\,\mathrm{d}x.
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