Results 1 to 2 of 2

Math Help - Posterior p.f.

  1. #1
    Junior Member
    Joined
    Dec 2008
    Posts
    37

    Posterior p.f.

    Suppose that the proportion Theta of defective items in a large manufactured lot is known to be either .1 or .2 and the prior p.f. of Theta is as follows:
    E(.1)=.7 and E(.2)=.3
    ^Those E's are a greek letter in the text, I'm guessing representing a prior distribution.
    Suppose also that when 8 items are selected at random from the lot, it is found that exactly two of them are defective. Determine the posterior p.f. of Theta.

    Any help?? This is our first day doing this so I am very lost...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Oct 2009
    Posts
    340
    First, let X denote the number of defectives in our sample of 8. Then, X|theta ~ Bin(8, theta), clearly; using Bayes rule, we get
    \displaystyle<br />
\xi(\theta|x) = \frac{\xi(\theta)f(x|\theta)}{f(x)}<br />

    With this, we now solve the problem in two steps. First, we need f(2), which we get via
    \displaystyle<br />
f(2) = \sum_{\theta \in \{.1, .2\}} \xi(\theta)f(2|\theta).<br />
    Once you have this, just calculate xi(.1|2) and xi(.2|2), and you are done.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. what dose the posterior mean?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 16th 2011, 05:44 PM
  2. Replies: 6
    Last Post: March 24th 2011, 05:57 PM
  3. Posterior distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: February 24th 2010, 12:59 PM
  4. Posterior distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 17th 2010, 04:10 AM
  5. posterior
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 11th 2009, 04:02 PM

Search Tags


/mathhelpforum @mathhelpforum