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Is this true?

  1. Aug 24, 2012 #1
    Hello,

    Suppose X is a Chi-square random variable. Then what is:

    [tex]\text{Pr}\left\{X<b\right\}[/tex]?

    Does the above probability is the CDF of X? The only difference is that there is no equality!

    Thanks
     
  2. jcsd
  3. Aug 24, 2012 #2

    Bacle2

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  4. Aug 24, 2012 #3
    My question can we say that Pr[X<b] approximately equal Pr[X<=b]?
     
  5. Aug 24, 2012 #4
    P(X < b) = P(X <= b) for continuous distributions, for example the chi-square distribution.
     
  6. Aug 24, 2012 #5

    D H

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    Not approximately equal. Exactly equal.

    The only time this isn't the case is with those non-continuous random variables for which P(x=b) can be non-zero for some values of b. This doesn't apply to the chi square distribution, which is an absolutely continuous probability distribution. "Absolutely continuous" essentially means it has a PDF; this a stronger constraint than merely being continuous.
     
  7. Aug 24, 2012 #6
    Thanks awkward and D_H, that is really relieving, since in my analysis I have Pr[X<b], and I was afraid it won't be correct to equate this with the CDF of Chi-square, i.e., Pr[X<=b], which has a closed form.

    Thanks all
     
  8. Aug 24, 2012 #7

    Bacle2

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    Just a quick comment: one of the obstacles to assigning non-zero probability to

    singletons is that an uncountable sum cannot converge unless only countably-many

    terms are non-zero.
     
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