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Math Help - probability density

  1. #1
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    Question probability density

    Suppose X has density f(x) = c/(x^4) for x > 1, and f(x) = 0 otherwise, where c is a constant. Find a) c; b) E(X); c) Var(X).

    I'm so confused...I dont even know where to start...

    Thanks in advance!
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  2. #2
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    Mar 2009
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    So the integral of f(x) over all x equals 1 (since its a probability density function) so
    \int_{1}^{\infty} \frac{c}{x^4} dx=1 so you need to integrate, then solve for c.

    E(X) = \int_{1}^{\infty} x \cdot \frac{c}{x^4} dx
    and
    Var(X) = E(X^2)-(E(X))^2
    So you can use a similiar process to find E(X^2)=\int_{1}^{\infty} x^2 \cdot \frac{c}{x^4} dx
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