Results 1 to 2 of 2

Math Help - Erlang Distribution

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    8
    From gamma distribution:
    α (alpha) is a positive integer n
    B (beta) is 1/λ

    so we have:
    f(x;y,n)=λ*(λx)^(n-1)*e^(-λx) / (n-1)!

    NOTE: I USED y instead of λ in the math code because I get an error otherwise.

    It can be shown that if the times between successive events are independent, each with an exponential distribution with parameter λ, then the total time X that elapses before all of the next n events occur has pdf f(x;λ,n).

    1.
    What is the expected value of X?
    my work: E(X) = αB = n*1/λ = n/λ

    If the time (in minutes) between arrivals of successive customers is exponentially distributed with λ = .5, how much time can be expected to elapse before the tenth customer arrives?
    This is more than likely wrong, but I don't know how to approach this problem: f(x;y,n)=f(n/y;y,n)=(y * (y*n/y)^(n-1)*e^(-y*n/y)) /(n-1)! = (y(n)^(n-1)e^(-n))/(n-1)! = (.5(10)^(10-1)e^(-10))/(10-1)! = .06

    2.
    If customer inter arrival time is exponentially distributed with λ = .5, what is the probability that the tenth customer (after the one who has just arrived) will arrive within the next 30 min?
    Think this is right: f(x;y,n)=f(30;y,n)=integral(0,30) (.5(.5x)^(10-1)e^(-.5x))/(10-1)! = .93

    3.
    The event [X ≤ t] occurs if at least n events occur in the next t units of time. Use the fact that the number of events occuring in an interval of lenth t has a Poisson distribution with parameter λt to write an expression (involving Poisson possibilities) for the Erlang cdf F(t; λ, n) = P(X ≤ t)
    lost one this one..
    Last edited by hansel13; July 29th 2009 at 08:43 PM. Reason: Merged posts
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jun 2009
    Posts
    8
    Mods can lock this, I don't need help anymore. Thanks.
    Last edited by hansel13; July 30th 2009 at 11:01 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: May 12th 2011, 03:43 PM
  2. Prove using the inverse of the Erlang-B loss function
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: May 13th 2010, 01:05 AM
  3. Prove using the inverse of the Erlang-B loss function
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: May 12th 2010, 02:54 AM
  4. Erlang Help
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 15th 2009, 04:49 PM
  5. Using Erlang C to solve for Staff
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: August 3rd 2009, 02:07 PM

Search Tags


/mathhelpforum @mathhelpforum