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Math Help - basic question on distribution equations

  1. #1
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    Exclamation basic question on distribution equations

    if i have a exponential distribution equation for example, and i want to know the probability of a certain region between x1 and x2, would all i have to do is get the cdf equation, then plugin lambda, then subtract this equation with a x2 value, with the same equation with a x1 value, to get the probability between x1 and x2?

    so

    and of course i set lamdba.
    cdf(x2) - cdf(x1) = probability between x1 and x2?

    Does this work with any distribution equation weather discrete or continuous?
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  2. #2
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    You need to be careful with your definition of "between x1 and x2" for the discrete case. The following is true for any discrete or continuous distribution:

    P(a < X \leq b) = cdf(b) - cdf(a)

    for most* continuous variables, its true that
     P(a < X) = P (a \leq X) and so you can say

    P(a \leq X \leq b) = cdf(b) - cdf(a) for those cases

    *some continuous variables are on a mixed distribution has a probability mass at a fixed point, so the last part may not work for those.
    Last edited by SpringFan25; April 8th 2011 at 03:53 PM.
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