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Help with linear independent and correlation

  1. Aug 3, 2009 #1
    1 Let X be a normal variable with mean 0 and variance 1. Let Y = ZX
    where Z and X are independent and Pr(Z = +1) = Pr(Z = -1) =1/2.

    a Show that Y and Z are independent.
    b Show that Y is also normal with mean 0 and variance 1.
    c Show that X and Y are uncorrelated but dependent.
    d Can you write down the joint density of X and Y ? Explain your
    answer.

    Note that this example exhibits two random variables which are un-
    correlated, normally distributed, but not independent (and necessarily
    not jointly normally distributed).

    Please help me with the bold questions.....
     
  2. jcsd
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