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Math Help - PDF of a random variable

  1. #1
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    PDF of a random variable

    The pdf of a random variable X is given by f(x)=c(1-x^2) for x element of (-1,1) (the element of symbol that looks like a curved E). For which values of c is this function actually a pdf? (c being a constant)

    I know that in order for something to be a pdf it must meet the requirements that
    p(x)>or= 0 for all x
    and
    the probabilities must sum to 1.

    Where I am confused is by the element of (-1,1) I am not sure how to solve this with an interval.
    Thanks to anyone who can help.
    (I attached the equation in a word doc just in case my notation above is confusing)
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  2. #2
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    Re: PDF of a random variable

    Quote Originally Posted by acasas4 View Post
    The pdf of a random variable X is given by f(x)=c(1-x^2) for x element of (-1,1) (the element of symbol that looks like a curved E). For which values of c is this function actually a pdf? (c being a constant)

    I know that in order for something to be a pdf it must meet the requirements that
    p(x)>or= 0 for all x
    and
    the probabilities must sum to 1.

    Where I am confused is by the element of (-1,1) I am not sure how to solve this with an interval.
    Thanks to anyone who can help.
    (I attached the equation in a word doc just in case my notation above is confusing)
    Since this is a continuous random variable the way that you check that it "sums" to 1 is to use an integral. That is what you need an interval!

    This must hold.

    \int_{-1}^{1}f(x)dx=1

    Evaluate the integral and solve for c.
    Last edited by TheEmptySet; October 20th 2011 at 01:23 PM. Reason: I can't spell aparently
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