Results 1 to 2 of 2

Math Help - maximum likelihood

  1. #1
    Member
    Joined
    May 2011
    Posts
    169

    maximum likelihood

    An individual taken from a very large biological population is of type A with probability p=0.5(1+t) and of type B with probabiliy 1-p=0.5(1-t).

    a) Suppose that X denotes the number of type A individuals in a random sample of size n. What is the probability that X = x?

    My answer: 0.5^x*(1+t)^x*(1-t)^{(n-x)} Classic binomial situation.

    b)Find the maximum likelihood estimator of t and show that it is unbiased.

    My answer: Find log likelihood, differentiate yields
    2x-n(1+t)/[(1+t)(1-t)]

    setting to zero yields t=(2x-n)/n

    To show unbiased, I need to find E(t). This is an integral including 0.5^x*(1+t)^x*(1-t)^{(n-x)} which I have no idea how to integrate.

    Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    May 2010
    Posts
    1,030
    Thanks
    28

    Re: maximum likelihood

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Maximum likelihood
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: December 20th 2011, 01:17 AM
  2. Maximum Likelihood
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 10th 2011, 01:14 PM
  3. Maximum Likelihood.
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 15th 2009, 07:54 AM
  4. Maximum likelihood
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 24th 2009, 03:04 PM
  5. Maximum Likelihood
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 20th 2009, 05:45 AM

Search Tags


/mathhelpforum @mathhelpforum