Results 1 to 3 of 3

Thread: Cumulative distribution function

  1. #1
    Newbie
    Joined
    Feb 2018
    From
    UK
    Posts
    8

    Cumulative distribution function

    Dear all, I have a question
    Given this distribution function:
    0 , x<0
    5/12x - 1/24x^2 , 0<x<4
    1 , x>4

    I want to find P(X<2)
    The answer gives it as 0.667 but why?
    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,793
    Thanks
    3035

    Re: Cumulative distribution function

    X= 2 is between 0 and 4 so we evaluate $\frac{5}{12}(2)- \frac{1}{24}(4)= \frac{5}{6}- \frac{1}{6}= \frac{4}{6}= \frac{2}{3}$ which, reduced to three decimal places, is approximately 0.667.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,796
    Thanks
    2827
    Awards
    1

    Re: Cumulative distribution function

    Quote Originally Posted by bbear123 View Post
    Dear all, I have a question
    Given this distribution function:
    0 , x<0
    5/12x - 1/24x^2 , 0<x<4
    1 , x>4
    I want to find P(X<2)
    The answer gives it as 0.667 but why?
    $CDF(x)=\begin{cases}0 &: x\le 0 \\ \frac{5}{12}x-\frac{1}{24}x^2 &: 0<x\le 4\\ 1 &:4<x\end{cases}$ This is the cumulative distribution function.
    The idea is that the function increases(accumulates) from zero to one from left to right.
    We define $\mathscr{P}(X)\le x)=CDF(x)$. More generally $\mathscr{P}(a\le X\le b)$ is $CDF(b)-CDF(a)$.

    Thus to answer your question: $\mathscr{P}(X\le 2)=CDF(2)$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cumulative Distribution Function
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: Jan 24th 2016, 08:11 PM
  2. cumulative distribution function using a gamma distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Sep 11th 2010, 10:05 AM
  3. Cumulative distribution function
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: Apr 9th 2010, 11:11 AM
  4. The cumulative distribution function
    Posted in the Statistics Forum
    Replies: 2
    Last Post: Nov 5th 2008, 03:02 AM
  5. Cumulative distribution function of binomial distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: Oct 31st 2008, 03:34 PM

Search Tags


/mathhelpforum @mathhelpforum