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Math Help - Statistics - PDF functions

  1. #1
    Junior Member
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    Aug 2008
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    Chicago, IL
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    Statistics - PDF functions

    wow my book is terrible and doesn't mention these types of problems...just assigns them.

    find the constant c for to make the following pdf function.
    a. f(x) = cx where x = 1, 2, ... , 25.
    b. f(x) = c(x+1)^3 where x = 0,1,2
    c. f(x) = c(1/3)^x where x= 1, 2, 3, ...

    i know what its asking for but i have absolutely no idea where to begin solving for c.
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    For the first function, you can input each of the values from 1 to 25 and your probabilities must sum to 1. This means that f(1) + f(2) + ... + f(24) + f(25) = 1. But f(x) = cx so c + 2c + ... + 24c + 25c = 1, or (1 + 2 + ... + 24 + 25)c = 1. Hence, you must calculate the sum of the numbers from 1 to 25, which is equal to \frac{25(1 + 25)}{2}.
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