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Math Help - Expectations question

  1. #1
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    Expectations question

    This has something to do with expectations and its properties.

    The sales per day for a product is estimated as follows based on past records

    Daily demand (X) / Probaility

    10 / .1
    11 / .2
    12 / .4
    13 / .3

    a. Obtain the mean and variance of the daily sales.
    b. If the porfit can be described by the equation, profit= -10+(4*X)

    What is the expected daily profit? What is the variance of the daily profit?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fobster
    This has something to do with expectations and its properties.

    The sales per day for a product is estimated as follows based on past records

    Daily demand (X) / Probaility

    10 / .1
    11 / .2
    12 / .4
    13 / .3

    a. Obtain the mean and variance of the daily sales.
    b. If the porfit can be described by the equation, profit= -10+(4*X)

    What is the expected daily profit? What is the variance of the daily profit?
    mean: \mu = \sum_i x_i.p(x_i) = (10\times 0.1)+(11 \times 0.2)+(12\times 0.4)+(13\times 0.3)

    variance: \sigma^2=\sum_i (x_i-\mu)^2\ p(x_i)

    expected daily profit: \mbox{E(profit)}=\sum_i (-10+4\times x_i)\ p(x_i)

    Var of profit: \mbox{E([profit-E(profit)]^2))}=\sum_i [(-10+4\times x_i)-\mbox{E(profit)}}]^2\ p(x_i)

    RonL
    Last edited by CaptainBlack; January 13th 2006 at 01:13 PM.
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  3. #3
    Newbie
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    Thanks for the help, I got these answers

    mean of the daily sales=11.9

    variance of the daily sales=0.89

    expected daily profit=37.6

    and the variance of the dialy profit was 14.24
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