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Plotting a Distribution

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data

    The distribution function of a real random variable X is given:

    F(x) =

    0 : x < 0
    x/2 : 0 ≤ x < 1
    2/3 : 1 ≤ x < 2
    11/12 : 2 ≤ x < 3
    1 : 3 ≤ x

    (a) Plot this distribution function.
    (b) What is P( X > 1/2 ) ?
    (c) What is P( 2 < X ≤ 4 ) ?
    (d) What is P( X < 3 ) ?
    (e) What is P( X = 1 ) ?

    3. The attempt at a solution

    Plotting was easy, but now i'm just unsure of my answers to the others.

    P( 2 < X < 4 ) = 1 - 2/3 = 1/3
    P( X = 1 ) = 2/3
    P( X > 1/2 ) = ??? This one confuses me.
    P( X < 3 ) = F(0) + F(1) + F(2) ??? Not sure if i need to be subtracting something here since this is wrong.
     
  2. jcsd
  3. Feb 25, 2013 #2
    For (b), use the fact that ##P(X > x) = 1 - P(X \le x)##.
     
  4. Feb 25, 2013 #3
    Ah, so it would essentially be 1 - P(x ≤ 1/2) which translates to 1 - 0.25 = 0.75, right?
     
  5. Feb 28, 2013 #4
    For question (d) would i just do the opposite of your formula and subtract 1 from P( X >= x )?
     
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