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Math Help - probability density function

  1. #1
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    Question probability density function

    suppose that X is a continuous random variable with probability density function given by

    f(X) = x^2 + (2/3)x +(1/3) for <or = x <or = c

    (a) what must be the value of c
    assuming this value of c , do the following :-

    b) plot f(x)
    c) compute and plot F(x)
    d)compute p(1/3 <or = X < or = 2/3 ) , E(X) , var (X)
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  2. #2
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    Quote Originally Posted by compufatwa View Post
    suppose that X is a continuous random variable with probability density function given by

    f(X) = x^2 + (2/3)x +(1/3) for <or = x <or = c

    (a) what must be the value of c
    assuming this value of c , do the following :-

    b) plot f(x)
    c) compute and plot F(x)
    d)compute p(1/3 <or = X < or = 2/3 ) , E(X) , var (X)
    Use \int_{0}^{c} f(x) \, dx = 1 and solve for c.

    Then check that f(x) \geq 0 over the interval 0 \leq x \leq c for the value of c that you find.
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