Results 1 to 2 of 2

Math Help - Exponential distribution qn

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    9

    Exponential distribution qn

    Hi, could someone help me out with this question?

    Calls to an emergency ambulance service in a large city are modeled by a Poisson process with an average 3.2 calls per hour.

    (a) what is the probability distribution of X where X is the length of time between successive calls?

    I'm saying it's an exponential distribution? But I'm not entirely sure...

    (b) find the E(X) = miu and Var(X) = sigma^2

    (c) find the probability that X is in the interval miu +/- 0.5sigma.

    I'm thinking if it were an exponential distribution, then I integrate the density function from the lower to the upper limits?

    (d) what is the probability that the time between successive calls to the ambulance service is longer than 30 minutes?

    (e) What is the probability that there will be at least one emergency ambulance service call in the next 45 minutes, given that there was no call in the last 15 minutes?

    Thanks in advance!
    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 deathstarx View Post
    Hi, could someone help me out with this question?

    Calls to an emergency ambulance service in a large city are modeled by a Poisson process with an average 3.2 calls per hour.

    (a) what is the probability distribution of X where X is the length of time between successive calls?

    I'm saying it's an exponential distribution? But I'm not entirely sure... Mr F says: Correct. In a poisson process the waiting times are exponentially distributed.

    If the number of arrivals in a given time interval [0,t] follows the Poisson distribution, with mean = λt, then the lengths of the inter-arrival times follow the Exponential distribution, with mean 1 / λ.
    (Quoted from Poisson distribution - Wikipedia, the free encyclopedia)


    (b) find the E(X) = miu and Var(X) = sigma^2

    (c) find the probability that X is in the interval miu +/- 0.5sigma.

    I'm thinking if it were an exponential distribution, then I integrate the density function from the lower to the upper limits?

    (d) what is the probability that the time between successive calls to the ambulance service is longer than 30 minutes?

    (e) What is the probability that there will be at least one emergency ambulance service call in the next 45 minutes, given that there was no call in the last 15 minutes?

    Thanks in advance!
    With the pdf found in (a), the rest should follow.

    For (e), calculate \Pr\left( \frac{1}{4} \leq X \leq 1 | X > \frac{1}{4} \right).
    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, 06:51 AM
  2. MLE for exponential distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 22nd 2011, 10:04 AM
  3. Exponential distribution.
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 20th 2010, 11:33 AM
  4. Replies: 0
    Last Post: March 14th 2010, 06:49 AM
  5. PDF exponential distribution
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: February 14th 2009, 08:34 PM

Search Tags


/mathhelpforum @mathhelpforum