Results 1 to 2 of 2

Math Help - Exponential and Gamma Distributions

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    6

    Exponential and Gamma Distributions

    Suppose the mean time to repair a computer has an exponential distribution with mean equal to 2 hours.
    a. Find P(repair > 2 hours)

    b. P(repair > 4 hours)

    c. How much time should be budgeted so that P(repair < budgeted time) ≥ .9?

    d. If Y = amount of time, and the repair costs $ = 50 + 100Y + Y2, what are the mean and SD of $?

    Five computers from the above problem need repair. Let T be the total time required to repair these five computers.
    a. Why does T have a gamma distribution?
    b. What are the mean and variance of T?

    c. Find P(T > 9) using the Poisson distribution.

    d. What would be the normal distribution approximation to P(T > 9)?

    e. Why is the normal distribution so inaccurate in this case?
    Last edited by mr fantastic; November 12th 2009 at 03:53 AM. Reason: Changed post title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ShaunW View Post
    Suppose the mean time to repair a computer has an exponential distribution with mean equal to 2 hours.
    a. Find P(repair > 2 hours)

    b. P(repair > 4 hours)

    c. How much time should be budgeted so that P(repair < budgeted time) ≥ .9?

    d. If Y = amount of time, and the repair costs $ = 50 + 100Y + Y2, what are the mean and SD of $?

    Five computers from the above problem need repair. Let T be the total time required to repair these five computers.
    a. Why does T have a gamma distribution?
    b. What are the mean and variance of T?

    c. Find P(T > 9) using the Poisson distribution.

    d. What would be the normal distribution approximation to P(T > 9)?

    e. Why is the normal distribution so inaccurate in this case?
    Tell us where you are having problems, and show us what you have done
    (we are not here to do your homework for you but to help you understand how to do it)

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: March 23rd 2011, 06:01 AM
  2. Question on exponential distributions
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 2nd 2010, 06:19 AM
  3. Exponential Distributions
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 18th 2009, 09:23 PM
  4. Poisson and exponential distributions
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: May 14th 2009, 10:58 PM
  5. Exponential distributions
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 22nd 2008, 12:41 AM

Search Tags


/mathhelpforum @mathhelpforum