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Math Help - Need help with this distribution

  1. #1
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    Need help with this distribution

    Below is the distribution function:

    F(x)=\frac{1}{4}1_{[0,\infty)}(x)+\frac{1}{2}1_{[1,\infty)}(x)+\frac{1}{4}1_{[2,\infty)(x)

    What does 1_{[1,\infty)}(x)...etc mean? Are they like some sort of indicator function? For example in this case, when x= 1/2, it's 0 and when x=3/2, it's 1.
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  2. #2
    MHF Contributor matheagle's Avatar
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    P(X=0)=.25

    P(X=1)=.5

    P(X=2)=.25

    You can see the jumps at those point, which are the probabilities.
    That is a sum of indicator functions that achieves one after 2.
    Both of you comments are wrong.
    At 1/2, only the first indicator is 1, hence F(.5)=1/4
    At 3/2, the first two indicators are 1, hence F(1.5)=1/4+1/2=3/4.
    Finally at 2 or afterwards F(x)=1/4+1/2+1/4=1
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  3. #3
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    Quote Originally Posted by matheagle View Post
    P(X=0)=.25

    P(X=1)=.5

    P(X=2)=.25

    You can see the jumps at those point, which are the probabilities.
    That is a sum of indicator functions that achieves one after 2.
    Both of you comments are wrong.
    At 1/2, only the first indicator is 1, hence F(.5)=1/4
    At 3/2, the first two indicators are 1, hence F(1.5)=1/4+1/2=3/4.
    Finally at 2 or afterwards F(x)=1/4+1/2+1/4=1
    Just Want to make sure I know what u mean.

    Suppose A=(-\frac{1}{2},\frac{1}{2}) The probability is
    F(\frac{1}{2})-F(-\frac{1}{2})=\frac{1}{4}. Is that true?
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  4. #4
    MHF Contributor matheagle's Avatar
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    1_{[0,\infty)}(x) is ONE if x is greater than or equal to 0.
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