Results 1 to 11 of 11

Math Help - Sample distribution of sample variance

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    19

    Sample distribution of sample variance

    I don't quite understand how this question is asking for, and how to do it.

    Consider the (small) population: 1,3,4,7

    Find the sampling distribution of sample variance(S^2), the sample variance when you take samples of size 2 with replacement.

    thank you for your help in advance
    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 shellshock View Post
    I don't quite understand how this question is asking for, and how to do it.

    Consider the (small) population: 1,3,4,7

    Find the sampling distribution of sample variance(S^2), the sample variance when you take samples of size 2 with replacement.

    thank you for your help in advance
    Well there are six samples of size 2, you can calculate the sample variance of all six and these each are equally likely so have probability 1/6.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    19
    Quote Originally Posted by CaptainBlack View Post
    Well there are six samples of size 2, you can calculate the sample variance of all six and these each are equally likely so have probability 1/6.

    CB
    Can you show me an example of how to calculate sample variance of one of them?? Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shellshock View Post
    Can you show me an example of how to calculate sample variance of one of them?? Thanks!
    Take the sample \{1,3\} its mean is 2, and its variance is:

    V(\{1,3\})=\frac{1}{2}\left( (1-2)^2+(3-2)^2\right)=1

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2009
    Posts
    19
    Quote Originally Posted by CaptainBlack View Post
    Take the sample \{1,3\} its mean is 2, and its variance is:

    V(\{1,3\})=\frac{1}{2}\left( (1-2)^2+(3-2)^2\right)=1

    CB
    Is it possible for the equation to be V(\{1,3\})=\frac{1}{2-1}\left( (1-2)^2+(3-2)^2\right)=2 ???? Because in my notes, the variance of a sample you have to minus 1 in the denominator. Also after I find all of the sample variance how do I find the sampling distribution of S^2? Do I just use the same equation, but use the mean of the results from all the sample variance instead?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shellshock View Post
    Is it possible for the equation to be V(\{1,3\})=\frac{1}{2-1}\left( (1-2)^2+(3-2)^2\right)=2 ???? Because in my notes, the variance of a sample you have to minus 1 in the denominator. Also after I find all of the sample variance how do I find the sampling distribution of S^2? Do I just use the same equation, but use the mean of the results from all the sample variance instead?
    It asks for sample variance not the estimate of the population variance, so I would use 1/2 not 1, but what you use is up to you so long as you say what you have done.

    CB
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2009
    Posts
    19
    Quote Originally Posted by CaptainBlack View Post
    It asks for sample variance not the estimate of the population variance, so I would use 1/2 not 1, but what you use is up to you so long as you say what you have done.

    CB
    O okay thank you, but how do i find the sample distribution of S^2?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shellshock View Post
    O okay thank you, but how do i find the sample distribution of S^2?
    You calculate s^2 for each of the six possible samples, and these each have a probability of 1/6.

    CB
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Oct 2009
    Posts
    19
    Quote Originally Posted by CaptainBlack View Post
    You calculate s^2 for each of the six possible samples, and these each have a probability of 1/6.

    CB
    Is there an equation for it? I'm sorry, this is the first time I'm doing sampling distribution.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by shellshock View Post
    Is there an equation for it? I'm sorry, this is the first time I'm doing sampling distribution.
    See the attachment for the calculation of the variance for each of the possible sample of size 2:

    Sample distribution of sample variance-gash.png

    So the sampling distribution for variance is v=0.25 with p=1/6, v=1 with p=1/6, v=2.25 with p=1/3, v=4 with p=1/6, v=9 with p=1/6.

    CB
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Oct 2009
    Posts
    19
    Quote Originally Posted by CaptainBlack View Post
    See the attachment for the calculation of the variance for each of the possible sample of size 2:

    Click image for larger version. 

Name:	gash.png 
Views:	34 
Size:	3.4 KB 
ID:	13871

    So the sampling distribution for variance is v=0.25 with p=1/6, v=1 with p=1/6, v=2.25 with p=1/3, v=4 with p=1/6, v=9 with p=1/6.

    CB
    Thank you very much!
    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. joint distribution of the sample mean and variance
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: March 3rd 2011, 11:50 PM
  3. pdf of sample variance?
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: January 21st 2010, 09:19 PM
  4. variance of sample mean and sample standard deviation
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: July 24th 2009, 06:20 AM
  5. Replies: 3
    Last Post: February 6th 2009, 04:59 AM

Search Tags


/mathhelpforum @mathhelpforum