Results 1 to 5 of 5

Math Help - PDF exponential distribution

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    12

    PDF exponential distribution

    Help please!

    Suppose that two electronic components in the guidance system for a missile operate independently and that each has a length of life governed by the exponential distribution with mean 1 (with measurements in hundreds of hours).
    Find the probability density function for the average length of life of the two components.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by kelli_rie View Post
    Help please!

    Suppose that two electronic components in the guidance system for a missile operate independently and that each has a length of life governed by the exponential distribution with mean 1 (with measurements in hundreds of hours).
    Find the probability density function for the average length of life of the two components.
    You need the pdf for U = \frac{X_1 + X_2}{2}. I'd just use a moment generating function approach to get this.

    Note: The pdf for the sum of i.i.d. exponential distributed random variables is the Erlang distribution (which is a special case of the gamma distribution).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by mr fantastic View Post
    You need the pdf for U = \frac{X_1 + X_2}{2}. I'd just use a moment generating function approach to get this.

    Note: The pdf for the sum of i.i.d. exponential distributed random variables is the Erlang distribution (which is a special case of the gamma distribution).
    I think this is probably a misinterpretation of the question.

    If we are interested in the distribution of the time to failure of the system, which has two failure modes with time to failure distributed exponentialy with mtbf t_1 amd t_2, then the time to failure of the system has an exponential distribution with mtbf t_3=[t_1^{-1} + t_2^{-1}]^{-1}.

    That is the failure rate for the system is the sum of the failure rates of the subsystems.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2008
    Posts
    12
    Quote Originally Posted by mr fantastic View Post
    You need the pdf for U = \frac{X_1 + X_2}{2}. I'd just use a moment generating function approach to get this.

    Note: The pdf for the sum of i.i.d. exponential distributed random variables is the Erlang distribution (which is a special case of the gamma distribution).
    Thank you so much. It seems so obvious now that you say it!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Correct, just use the product of Moment Generating Functions.
    Last edited by matheagle; February 14th 2009 at 09:26 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential Distribution
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 4th 2011, 05:51 AM
  2. MLE for exponential distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 22nd 2011, 09:04 AM
  3. Exponential distribution.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 20th 2010, 10:33 AM
  4. Replies: 0
    Last Post: March 14th 2010, 05:49 AM
  5. Exponential distribution qn
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: September 23rd 2009, 01:59 AM

Search Tags


/mathhelpforum @mathhelpforum