Results 1 to 2 of 2

Math Help - pdf of sample variance?

  1. #1
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303

    pdf of sample variance?

    Let Y_{1},Y_{2},...,Y_{n}~iid~N(\mu,\sigma).

    Q: Find the probability density function of S^{2}.

    I am not sure how to approach this problem. I tried using the mgf method, but failed to find a recognizable mgf. My teacher recomened that we use the transformation method to derive the pdf, but I not sure how with this function.

    Here is what he showed on the board.

    Let S^{2}=\frac{\sigma^{2}}{(n-1)}\frac{(n-1)S^{2}}{\sigma^{2}}. Then, treat the preceeding quantity like U=aY and use the tranformation method to find f_{U}(u).

    I really don't know where to go from here. Do I let U=s^{2}, a=\frac{\sigma^{2}}{(n-1)}, and Y=\frac{(n-1)S^{2}}{\sigma^{2}}?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Use \sum_{i=1}^n\left({X_i-\bar X\over \sigma}\right)^2\sim\chi^2_{n-1}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sample Variance
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 10th 2011, 11:49 AM
  2. Sample distribution of sample variance
    Posted in the Statistics Forum
    Replies: 10
    Last Post: November 16th 2009, 01:12 PM
  3. Sample variance
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 4th 2009, 03:21 AM
  4. Sample Variance
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: August 20th 2009, 04:33 PM
  5. variance of sample mean and sample standard deviation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 24th 2009, 06:20 AM

Search Tags


/mathhelpforum @mathhelpforum