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Simple question about expected value

  1. May 3, 2010 #1
    Hello,

    Just came across this that:

    E[cos(t)sin(t)] = 0

    the expected value of the product of cos(t)sin(t) is 0. However, I am unable to convince myself that is the case. Can anyone help me understand why this is so?

    Many thanks,

    Luc
     
  2. jcsd
  3. May 3, 2010 #2
    I suppose the probability space is [itex][0,2 \pi)[/itex] with normalized Lebesgue measure? In that case, what it means is
    [tex]
    \frac{1}{2\pi}\int_0^{2\pi} \sin(t) \cos(t)\,dt = 0
    [/tex]
     
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