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Math Help - Cumulative Distribution Function Question

  1. #1
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    Cumulative Distribution Function Question

    The C.D.F. (cumulative density function) of the random variable X is given by,

    F(x)= [0, x<0
    x/2, 0<=x<1
    2/3, 1<=x<2
    11/12, 2<=x<3
    1, 3<=x]

    a) Find P(X>1/2)

    b) Find P(2<X<=4)

    c) Find P(X=1)

    Does anyone know how to approach this?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by abc4616 View Post
    The C.D.F. (cumulative density function) of the random variable X is given by,

    F(x)= [0, x<0
    x/2, 0<=x<1
    2/3, 1<=x<2
    11/12, 2<=x<3
    1, 3<=x]

    a) Find P(X>1/2)
    Definition of the cdf, tells you that:

    P(X>1/2)=F(1/2).

    b) Find P(2<X<=4)
    Again from the definition of the sdf:

    P(2<X<=4)=P(X<=4)-P(X<2)=F(4)-F(2)

    c) Find P(X=1)
    This is equal to the jump in the cdf at x=1, so its F(1)-F(1-)=2/3-1/2=1/6

    RonL
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