Results 1 to 4 of 4

Math Help - Mean and Variance

  1. #1
    Junior Member
    Joined
    Jan 2010
    Posts
    52

    Question Mean and Variance

    The daily distance,X,covered by a bread seller in a housing estate from Monday to Friday has mean 12 km and standard deviation 0.5 km.For Saturday and Sunday,the daily distance,Y,covered by the bread seller has mean 10 km and standard deviation 0.4 km.

    Find mean and variance of the average daily distance,S,covered by the bread seller in 7 days from Monday to Sunday and state whatever assumptions you have made.

    I've calculated the mean of S to be 11.43 km from :

    S = [5X+2Y]/7
    E(S) = (5/7)E(X) + (2/7)E(Y)
    = (5/7)(12) + (2/7)(10)
    = 11.43 km

    Var(S) is given as

    Var(S) = (5/49)(0.5^2) + (2/49)(0.4^2)
    =0.032 km^2

    Shouldn't Var(S) = (25/49)(0.5^2) + (4/49)(0.4^2)
    = 0.141 km^2 ???

    In this case,we assume that the distance travelled by the bread seller on a certain day as independent of the distance travelled on other days isn't it?

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

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Okay, so exactly where did you need that assumption of independence?

    If they were not independent, what would you get for the variance?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    Posts
    52
    Quote Originally Posted by TKHunny View Post
    Okay, so exactly where did you need that assumption of independence?

    If they were not independent, what would you get for the variance?
    I have no idea.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    When you added the variances, and did not include a covariance term, this is where you assumed they were independent.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with variance
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 3rd 2011, 01:53 AM
  2. variance of the sample variance
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 8th 2011, 08:35 PM
  3. How to get new variance given old variance and average
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 23rd 2010, 05:39 AM
  4. Variance Help
    Posted in the Statistics Forum
    Replies: 2
    Last Post: August 23rd 2009, 01:22 PM
  5. Variance of the population variance.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 10th 2008, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum