Notices
Results 1 to 4 of 4

Thread: Poisson Process and Two Exponentials

  1. #1 Poisson Process and Two Exponentials 
    Forum Masters Degree Golkarian's Avatar
    Join Date
    Nov 2008
    Posts
    510
    I understand how a Poisson process works if you have many exponentials (like buses coming to a bus stop), but what about a finite number? For example two light bulbs fail according to the exponential distribution and I'm asked the probability one failing. How do I work the fact that their are two into the equation? Or does it matter? The parameter in the gamma distribution should be the number that fail, correct?


    Reply With Quote  
     

  2.  
     

  3. #2  
    Forum Professor wallaby's Avatar
    Join Date
    Jul 2005
    Location
    Australia
    Posts
    1,521
    The number of random events occurring within a defined time interval follow a Poisson distribution, so the number of light bulbs that fail each month would be an example of a Poisson Random Variable. While the time between random events follows an exponential distribution, the time until failure of each light bulb for instance. So if you want the probability of both light bulbs failing in a particular time interval you must use the Poisson distribution, the parameter in this distribution will be the average number of light bulb failures per unit of time being considered and this information can be determined from the average time for 1 light bulb to fail.


    Reply With Quote  
     

  4. #3  
    Forum Masters Degree Golkarian's Avatar
    Join Date
    Nov 2008
    Posts
    510
    So when using the gamma distribution to find the probability of say 2 failing in a given time, I use k=2 (using the pdf from wikipedia), and don't care about the fact that there are only 2?
    Reply With Quote  
     

  5. #4  
    Forum Professor wallaby's Avatar
    Join Date
    Jul 2005
    Location
    Australia
    Posts
    1,521
    Use the PDF for the Poisson distribution,



    For x = 2 and lambda being the rate parameter i mentioned previously.
    Reply With Quote  
     

Similar Threads

  1. Replies: 5
    Last Post: April 19th, 2010, 07:09 PM
  2. Poisson distribution
    By Heinsbergrelatz in forum Mathematics
    Replies: 1
    Last Post: January 15th, 2010, 05:19 PM
  3. Haber Process Plant
    By emetzner in forum Chemistry
    Replies: 16
    Last Post: January 28th, 2009, 11:57 AM
  4. How to solve the screened poisson Equation in 2D?
    By allyouneedispop in forum Mathematics
    Replies: 2
    Last Post: January 27th, 2009, 03:29 PM
  5. Chloralkali Process
    By The P-manator in forum Chemistry
    Replies: 0
    Last Post: September 4th, 2006, 05:25 PM
Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •