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Thread: existence of moments question

  1. #1
    Apr 2010

    existence of moments question

    I was ready the book "Introduction to probability theory" by James R. McCord, III [and] Richard M. Moroney, Jr and it gave this thereom about the existence of moments: if the mth raw moment of a random variable X exists, then the Xth and all preceding moments of X about any finite point all exist.
    It then said that this follows from simple computations and the relation:
    E(|X|^(m-1))≤|X|^(m + 1)
    Which is true because: |x|^(m-1)≤|x|^(m+1).
    For all real x and all m≥1.

    I am not understanding any of this at all!!! Can someone help explain to me what is going on?
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  2. #2
    MHF Contributor matheagle's Avatar
    Feb 2009
    If I understand what you're asking, because the XTH moment statement seems to be a typo

    Just use calculus... If f<g, then $\displaystyle \int f<\int g$
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