Results 1 to 3 of 3

Math Help - gamma dist

  1. #1
    Senior Member sfspitfire23's Avatar
    Joined
    Oct 2009
    Posts
    273

    gamma dist

    Hey guys-been struggling with this question the whole day-

    Weekly downtime X (in hrs) for a certain industrial machine has approximately a gamma dist. with alpha=3.5 and beta=1.5. Loss L (in dollars) as a result of this downtime is given by L=30X+2x^2.

    What is the expected value and variance of L?

    So, I first set out to find an equation for E(X^k) and I ended up with \frac{\beta^k \Gamma(\alpha+k)}{\Gamma(\alpha)} and I am unsure how to proceed from here. Also, is my derivation correct?
    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 sfspitfire23 View Post
    Hey guys-been struggling with this question the whole day-

    Weekly downtime X (in hrs) for a certain industrial machine has approximately a gamma dist. with alpha=3.5 and beta=1.5. Loss L (in dollars) as a result of this downtime is given by L=30X+2x^2.

    What is the expected value and variance of L?

    So, I first set out to find an equation for E(X^k) and I ended up with \frac{\beta^k \Gamma(\alpha+k)}{\Gamma(\alpha)} and I am unsure how to proceed from here. Also, is my derivation correct?
    \displaystyle E(L) = 30 E(X) + 2 E(X^2). I haven't time to check your expression for E(X^k) but I'm sure there are websites that would either confirm or deny the result.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    In order to obtain the variance of L, first obtain it's second moment.

    E(L^2)=900E(X^2)+120E(X^3)+4E(X^4)

    Remember that the beta can either be in the numerator or denominator, depending on how you write your density.
    The technique is easy. OR just the MGF and differentiate.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the best unbiased estimator of 1/b of gamma dist.
    Posted in the Advanced Statistics Forum
    Replies: 13
    Last Post: May 3rd 2011, 04:15 AM
  2. Gamma - Gamma parameter estimation EM algorithm
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: July 24th 2010, 09:53 AM
  3. hypothesis test gamma dist
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 4th 2009, 08:19 AM
  4. beta and gamma dist
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 2nd 2009, 12:52 AM
  5. Replies: 0
    Last Post: March 30th 2008, 12:44 PM

Search Tags


/mathhelpforum @mathhelpforum