Results 1 to 3 of 3

Math Help - CDF of random summation of exponential radom variables

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    1

    CDF of random summation of exponential radom variables

    Given X=\sum_{i=1}^N Z_i, where N is a random variable, and Z_i are i.i.d. exponential random variable with rate 1, N and Z_i are independent. What's the relationship between the CDF of X and the CDF of N? Do we have any closed form relations or bounds between them?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I don't think I've ever seen this b4, but you will need to know the relationship between the Z's and N, like if they are independent. Then I would think you'd attack the problem via...
    P\{Z_1+\cdots +Z_N\le a\}=P\{Z_1+\cdots +Z_n\le a|N=n\}P\{N=n\}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    It is possible to prove that G_{X}(s)=G_N \circ G_{Z_1}(s), where G_X is the probability generating function of the r.v. X.

    I haven't found a relationship between the CDF and the PGF, but maybe you can ^^
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Independent exponential random variables
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: December 12th 2011, 08:31 AM
  2. Exponential Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: December 7th 2010, 05:32 PM
  3. The difference of exponential random variables
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: April 15th 2009, 05:01 PM
  4. Exponential Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 29th 2008, 01:43 AM
  5. Hyper-exponential Random Variables
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 29th 2008, 01:29 AM

Search Tags


/mathhelpforum @mathhelpforum