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Math Help - distribution of a continuous random variable X is symmetric

  1. #1
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    distribution of a continuous random variable X is symmetric

    The distribution of a continuous random variable X is symmetric about the value c if the pdf f(x) of X is such that f(c − x) = f(c + x) for all real numbers x.
    (a) Show that if X is symmetric about 0, both the mean and the median of X are 0.

    Any help would be greatly appreciated
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  2. #2
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    Re: distribution of a continuous random variable X is symmetric

    Do you know what the mean and median are? If you were given the distribution function, f, how would you find the mean? How would you find the median?
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  3. #3
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    Re: distribution of a continuous random variable X is symmetric

    Well, the median is F(x)=0.5, for the cdf, and the mean could be found by finding the mgf and the first moment about 0, or by finding the integral of xf(x) with limits infinity and -infinity. How would this information help in the proof?
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