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Math Help - density function

  1. #1
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    density function

    Q#1 A continuous random variable X has the density function
    f(x)=x for 0<x<1
    2-x for 1_<x<2
    0 elsewhere



    a. Show that P(0<X<2)=1
    b. Find P(X<1.2).
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by nisoo-1 View Post
    Q#1 A continuous random variable X has the density function
    f(x)=x for 0<x<1
    2-x for 1_<x<2
    0 elsewhere



    a. Show that P(0<X<2)=1
    <br />
P(0<x<2) = \int_0^2 f(x) ~dx = \int_0^1 x ~dx + \int_1^2 (2-x)~dx= 1/2 + 1/2=1<br />

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by nisoo-1 View Post
    Q#1 A continuous random variable X has the density function
    f(x)=x for 0<x<1
    2-x for 1_<x<2
    0 elsewhere




    b. Find P(X<1.2).
    <br />
P(x<1.2) = \int_0^{1.2} f(x) ~dx = \int_0^1 x ~dx + \int_1^{1.2} (2-x)~dx = 1/2 + \left[ 2x-x^2/2\right]_1^{1.2}

    RonL
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  4. #4
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    Calculus may be a bit much for this problem. If you are supposed to use it, fine, but please keep in mind there may be other ways of going about things. In this case, if you know a little about right triangles it is just as straight-forward.
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