1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook