Results 1 to 2 of 2

Math Help - Probability question!

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    2

    Thumbs up Probability question!

    Hey guys,

    Urgent help needed!

    A computerized switch board in the telephone exchange receives an average 4 calls per minute. Find the probability that

    (a) the interval of time between successive calls at any time is less than 10 seconds.

    (b) at least 5 calls are received in one minute.

    Thanks a million!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303
    Quote Originally Posted by mathask View Post
    Hey guys,

    Urgent help needed!

    A computerized switch board in the telephone exchange receives an average 4 calls per minute. Find the probability that –

    (a) the interval of time between successive calls at any time is less than 10 seconds.

    (b) at least 5 calls are received in one minute.

    Thanks a million!
    a) It sounds like an exponential distribution with mean \frac{1}{4} (minutes/calls). So, the probability the interval of time between calls is less that 10 seconds (or equivalently, 1/6 of a minute) is

    P(Y<\frac{1}{6})=<br />
\int_{0}^{\frac{1}{6}}\frac{1}{4}e^{-\frac{y}{4}}dy.

    b) Now, instead of the time between events we are interested in the number of events in a given time interval. So, your random variable Y is poisson with mean \lambda=4. So, the probability is

    P(Y\geq\\5)=\sum_{y=5}^{\infty} \frac{\lambda^{y}e^{-\lambda}}<br />
{y!}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: February 10th 2013, 02:11 PM
  2. Probability question :)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 12th 2011, 02:55 PM
  3. Probability question involving (A given B type question )
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 9th 2009, 09:08 AM
  4. Probability Question
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 21st 2009, 05:28 PM
  5. A probability question and an Expectations question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 29th 2006, 06:13 PM

Search Tags


/mathhelpforum @mathhelpforum