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Cumulative Distribution function

  1. Jun 7, 2009 #1
    1. The problem statement, all variables and given/known data

    I have been given a CDF of T value probabilites for t >= 0
    I have been given P(t=3)=0.59 P(t=5)=0.85


    2. Relevant equations



    3. The attempt at a solution

    I have been asked to find P(T > 5 | T>3 )

    I was wondering how to work this out.

    As this is a conditional probabilty I was heading towards

    P(T > 5 | T>3 ) =
    [itex]
    \frac{P(T > 5 \and T>3 )}{P(t>5)}[/itex]
    so the probabilty of P(T > 5 \and T>3 )} = .41
    and P(t>5) = .15

    But you can't use that calculation.

    But wouldn't the probability of of being > 5 still just be .15

    Any help would be appreciated
     
  2. jcsd
  3. Jun 7, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, P(t> 5)= 1- .85= .15. But that is NOT "P(t>v5|P>3)"

    Remember the basic formula P(A and B)= P(A|B)P(B).

    Now if x> 5 then it MUST be >3 so P((x>.5) and (x>3))= P(x> 5).

    P(t>5)= P(t>5|P>3)P(t> 3).

    You know P(T>5) and you know P(t> 3). Put those into that formula and solve for P(t> 5|t> 3).
     
  4. Jun 7, 2009 #3
    Thanks for your help.

    So we need to find


    P(A|B) = P(A and B)/P(B)

    we have:

    P(t>5)= P(t>5|P>3)P(t> 3)

    and need to find

    P(t>5|P>3)= P(t>5)/P(t> 3)

    P(t>5|P>3)= P(0.15)/P(0.41)

    therefore

    P(t>5|P>3)= 0.365

    regards
     
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