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Math Help - Continuous random variable

  1. #1
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    Continuous random variable

    The mode of a continuous random variable X is 1 and this is a stationary point. Given that X takes values over the range [0, 3] find possible expression for:
    (a) the c.d.f. of X
    (b) the p.d.f. of X.
    --------------------------------------
    How could I find them?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by geton View Post
    The mode of a continuous random variable X is 1 and this is a stationary point. Given that X takes values over the range [0, 3] find possible expression for:
    (a) the c.d.f. of X
    (b) the p.d.f. of X.
    --------------------------------------
    How could I find them?
    Try letting the pdf be a cubic in x, with roots at x=0 and x=3, and a local maximum at x=1. Then normalise so that the integral from 0 to 3 is equal to 1.

    Then so long as the third root is not in the open interval (0,3) you have a pdf satisfying the given conditions, and from that you should be able to find the cdf.

    CB
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