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Math Help - Statistics - Discrete Random Variable

  1. #1
    Newbie Tom G's Avatar
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    Statistics - Discrete Random Variable

    Hi, i'm completly at a loss as to how to approach this question and don't know how to answer it, can someone help me please.

    The discrete random variable X has c.d.f. F(x) defined by

    F(x) = (2+x)/7 ; x = 1, 2, 3, 4 and 5

    a/ Find P(X<=3)
    b/ Show that P(X=4) = 1/7
    c/ Find the probability distribution for X.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Tom G View Post
    Hi, i'm completly at a loss as to how to approach this question and don't know how to answer it, can someone help me please.

    The discrete random variable X has c.d.f. F(x) defined by

    F(x) = (2+x)/7 ; x = 1, 2, 3, 4 and 5

    a/ Find P(X<=3)
    b/ Show that P(X=4) = 1/7
    c/ Find the probability distribution for X.
    F is a cdf - cumulative distribution function, so:

    P(X<=a)=F(a), a=1, 2, 3, 4, 5.

    a) Hence P(X<=3)=F(3)=5/7.

    b) P(X=4)=P(X<=4)-P(X<=3)=F(4)-F(3)=6/7-5/7=1/7

    c) P(X=1)=P(X<=1)=F(1)=3/7,
    P(X=2)=P(X<=2)-P(X<=1)=F(2)-F(1)=1/7

    and similarly: P(X=3)=1/7, P(X=4)=1/7.

    Finaly P(X=5)=1-P(X<=4)=1-6/7=1/7.

    RonL
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