My Math Forum Interpreting probability from a cumulative distribution

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 February 5th, 2017, 02:12 PM #1 Newbie   Joined: Feb 2017 From: Corpus Christi Texas Posts: 6 Thanks: 0 Interpreting probability from a cumulative distribution The discrete cumulative distribution I have is F(x)=( 0 for x<1, 1/3 for 1or=10) I'm asked to find P(2
 February 5th, 2017, 02:30 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 1,696 Thanks: 861 $F(x) = \begin{cases} 0 &x < 1 \\ \dfrac 1 3 &1\leq x < 5 \\ \dfrac 1 2 &4 \leq x < 6\\ \dfrac 5 6 &6 \leq x < 10 \\ 1 &10 \leq x \end{cases}$ Find $P[2 < x \leq 6]$ $P[6]=\dfrac 5 6$ $P[2] = \dfrac 1 3$ $P[2 < x \leq 6] = P[6]-P[2] = \dfrac 5 6 - \dfrac 1 3 = \dfrac 1 2$ You don't need to worry about overlap with the cumulative distribution function. If you were given the probability density function you would have to take care to evaluate each bit with the proper limits but by giving you the CDF they've already taken care of that for you.
 February 5th, 2017, 04:11 PM #3 Newbie   Joined: Feb 2017 From: Corpus Christi Texas Posts: 6 Thanks: 0 Oh that totally makes sense! You can just subtract by the bounds. Thanks alot bud. Btw how were you able to write out the function so nicely? Are there tools on this site or do you have a special kind of keyboard app?
February 5th, 2017, 06:16 PM   #4
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Quote:
 Originally Posted by Rramos2 Oh that totally makes sense! You can just subtract by the bounds. Thanks alot bud. Btw how were you able to write out the function so nicely? Are there tools on this site or do you have a special kind of keyboard app?
LaTex

February 5th, 2017, 08:22 PM   #5
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 Originally Posted by romsek LaTex
this is kinda neat

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