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Math Help - continuous random variable

  1. #1
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    continuous random variable

    The continuous random variable X has a probability density function defined as follows:

    f(x)= 1/4 , 0<=x<1,

    = 3/8 (3-x) , 1<=x<=3

    The pdf is not continuous at x=1 and probability density functions are only defined when they are a continuous function. So is the pdf given above valid?
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  2. #2
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    There are just two requirements:
    1) f(x)\ge0 and

    2) \int_{ - \infty }^\infty  {f(x)dx}  = 1.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by hooke View Post
    The continuous random variable X has a probability density function defined as follows:

    f(x)= 1/4 , 0<=x<1,

    = 3/8 (3-x) , 1<=x<=3

    The pdf is not continuous at x=1 and probability density functions are only defined when they are a continuous function. So is the pdf given above valid?
    No they are allowed to be discountinuous. The requirement is that it be positive, (Lebesgue) integrable, and integrate up to 1.

    CB
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    Quote Originally Posted by CaptainBlack View Post
    No they are allowed to be discountinuous. The requirement is that it be positive, (Lebesgue) integrable, and integrate up to 1.

    CB
    Thanks CB and Plato, how about the cummulative distribution function? Must it be continuous?
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  5. #5
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    Quote Originally Posted by hooke View Post
    Thanks CB and Plato, how about the cummulative distribution function? Must it be continuous?
    Yes, its a consequence of the defining integral.

    CB
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