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Math Help - probability density function question

  1. #1
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    Question probability density function question

    hey,

    question

    Suppose the probability density function of the length of computer cables is
    f(x) = 0.1 from 1200 to 1210 millimeters.

    (1.) Determine the mean and standard deviation of the cable length.

    I understand how to do p.d.f if you have to variance and so forth but I dont understand this one.

    Thanks any help appreciated
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  2. #2
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    Quote Originally Posted by Alicia View Post
    hey,

    question

    Suppose the probability density function of the length of computer cables is
    f(x) = 0.1 from 1200 to 1210 millimeters.

    (1.) Determine the mean and standard deviation of the cable length.

    I understand how to do p.d.f if you have to variance and so forth but I dont understand this one.

    Thanks any help appreciated
    Read this: Uniform distribution (continuous - Wikipedia, the free encyclopedia)
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Here's a derivation for the general uniform distribution:

    Let X be a random variable with pdf f(x) = \frac{1}{b-a} for a \leq x \leq b and zero elsewhere.


    By definition: \bar{X} = \int_{a}^{b} \frac{x}{b - a} \, dx = \left( \frac{b^2 - a^2}{2} \right) \, \frac{1}{b - a} = \frac{b + a}{2}.


    By definition: E(X^2) = \int_{a}^{b} \frac{x^2}{b - a} \, dx = \left( \frac{b^3 - a^3}{3} \right) \, \frac{1}{b - a} = \frac{b^2 + ab + a^2}{3}.


    By definition: Var(X) = E(X^2) - \bar{X}^2


    = \left( \frac{b^2 +ab + a^2}{3} \right) - \frac{(b + a)^2}{4} = \frac{4(b^2 + ab + a^2) - 3(b^2 + 2ab + a^2)}{12}


     = \frac{b^2 - a^2 - 2ab}{12} = \frac{(b - a)^2}{12}.

    In your problem, a = 1200 and b = 1210 .....
    Last edited by mr fantastic; April 24th 2008 at 04:12 AM. Reason: Added the last line.
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