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[Probability] question

  1. Mar 29, 2010 #1
    let be a Random variable X with a probability defined by a positive measure

    [tex] P(X\lex ) =\int_{-\infty}^{x}dt\mu(t) [/tex]

    so [tex] \mu (x) \ge 0 [/tex] for every Real number [tex] \mu (x) =\mu(-x) [/tex] (even measure) and

    [tex] 1 =\int_{-\infty}^{\infty}dt\mu(t) [/tex] (normalization)

    my question is , is there any way to proof that the Polynomial

    [tex] 1+\frac{E(t^{2})}{2!}x^{2}+\frac{E(t^{4})}{4!}x^{4}+\frac{E(t^{6})}{6!}x^{6}+\frac{E(t^{8})}{8!}x^{8}+ ..... =E(exp(tx) [/tex]

    has ONLY pure imaginary roots ?? , for example if the measure is '1' defined on (-1,1) then we have [tex]sinh(x)/x [/tex] which have only pure imaginary roots.
  2. jcsd
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