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Why is it P(X=a) = 0 for all a belonging to ℝ for continuus rand.vars?

  1. Mar 28, 2013 #1
    I probably miss something basic, unless it's an abstract definition.
     
  2. jcsd
  3. Mar 28, 2013 #2

    HallsofIvy

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    [tex]P(X\in [a, b])= \int_a^b f(x)dx[/tex]
    where f(x) is the "probability density function".

    P(X= a) means [tex]P(X \in [a,a])= \int_a^a f(x)dx= 0[/tex]
     
  4. Mar 28, 2013 #3
    Thank you. I guess it's like my initial assumption: "it represents an atomic elelement of the integral and that tends to 0".
     
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