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Math Help - a question about the standard deviation of the function of a random variable

  1. #1
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    a question about the standard deviation of the function of a random variable

    Hi all,

    I'm having trouble with the last part of this question:
    I have the profit formula g(X) as a function of X the random variable determined by the cost of the further work:

    g(X)=1.1X + 1.1(20)

    g(X)=1.1X + 22

    so E(g(X))=1.1(4) + 22 = 26.4million

    the s.d is the root of the variance var(g)= (a^2)(var(X)) for aX+b

    so my calculations give the variance as (1.1^2)(1^2) = 1.21

    so s.d = 1.1 million

    but the answer in the back of the book is 1million.

    Would someone be able to tell me where I am going wrong???
    Many thanks!
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  2. #2
    MHF Contributor
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    Re: a question about the standard deviation of the function of a random variable

    Hey flashylightsmeow.

    The profit will be 10% of his expected costs, so if the expected cost is say h(X), then g(X) will be 0.1*h(X). Retry the problem by getting the profit function as a separate function of the total costs (the profit (remember the profit will be 10% of the costs so if the total cost is to be 100 million, then the profit will be 10 million).
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  3. #3
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    Re: a question about the standard deviation of the function of a random variable

    Dear Chiro, thank you very much for your help!!
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