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Math Help - another continuos random variable

  1. #1
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    another continuos random variable

    if X is a continuous random variable defined as:

    f(x) = {
    1/16x + 1/4, -4 <= x <= 0
    -1/16x + 14, 0 <= x <= 4
    }

    a) what is the 0.8 quantile?
    b) 45th percentile?

    I know the basic premise of the question, but being defined in 2 parts is what eludes me.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by scorpion007 View Post
    if X is a continuous random variable defined as:

    f(x) = {
    1/16x + 1/4, -4 <= x <= 0
    -1/16x + 14, 0 <= x <= 4
    }

    a) what is the 0.8 quantile?
    b) 45th percentile?

    I know the basic premise of the question, but being defined in 2 parts is what eludes me.
    Lets assume f is the density.

    a) The 0.8 quantile is y such that p(x<y)=0.8, or:

    int(-4, y) f(x) dx=0.8.

    Now we know that int(-4,0) f(x) dx=0.5, so we want y such that:

    int(0,y) f(x) dx=int(0,y) {-1/16x + 14} dx =0.3

    b) same as befor except that 0.8 is replaced by 0.45, also as 0.45<0.5
    we are on the other bit of the definition so:


    The 45th percentile is the 0.45 quantile so we seek a y such that p(x<y)=0.45, or:

    int(-4, y) f(x) dx=0.45.

    or

    int(-4,y) f(x) dx=int(-4,y) {1/16x + 14} dx =0.45

    RonL
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