Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is this true?

  1. Aug 24, 2012 #1

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


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

  2. jcsd
  3. Aug 24, 2012 #2


    User Avatar
    Science Advisor

  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

    User Avatar
    Staff Emeritus
    Science Advisor

    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


    User Avatar
    Science Advisor

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook