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Math Help - Density

  1. #1
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    Density

    Suppose that X is a random variable whose density is f(x) = 1 / [2*(1 + |x|)^2] , (- inf < x< inf)

    a) Draw the graph of f(x)
    b) Find P(-1 < X < 2)
    c) Find P(|X| > 1)
    d) Is E(X) defined?

    So I don't know about the other parts, but for part b is it just something like the integral from -1 to 2 of f(x)? Thanks for any help!!
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  2. #2
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    Quote Originally Posted by bart203 View Post
    Suppose that X is a random variable whose density is f(x) = 1 / [2*(1 + |x|)^2] , (- inf < x< inf)

    a) Draw the graph of f(x)
    b) Find P(-1 < X < 2)
    c) Find P(|X| > 1)
    d) Is E(X) defined?

    So I don't know about the other parts, but for part b is it just something like the integral from -1 to 2 of f(x)? Thanks for any help!!
    Yes.

    For each part, just apply the usual definition and crank out the calculation. Note that |x| = x for x > 0 and -x for x < 0. Please show all your work and say where you get stuck if you need more help.
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