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January 13th, 2013, 08:13 PM  #1 
Senior Member Joined: Sep 2011 Posts: 140 Thanks: 0  Statistics
When proving the strong law of large numbers, there is one step where i am confused (the most first step infact...) , and . To bound , note that we can write : Could anyone please explain clearly on what the heck is going on here? i have no idea why becomes that above, with all different letters i,j,k,l...... i would appreciate the help 
January 14th, 2013, 01:55 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  Re: Statistics
It is simply a multinomial expansion. The terms where all the X's are different get canceled by the mean.

January 14th, 2013, 03:12 PM  #3 
Senior Member Joined: Sep 2011 Posts: 140 Thanks: 0  Re: Statistics
Sorry could you please explain what you mean by the means cancelling out?, and i just dont get how it becomes like the expression above, through expanding what exactly?

January 15th, 2013, 01:05 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,807 Thanks: 717  Re: Statistics
I would rathen not use Latex (I still haven't got the hang of it). I will use Yk instead of X[hat]k Mutinomial expansion gives: (Y1 + Y2 + ... +Yn)^4 = {Y1^4 + Y2^4 + ....Yn^4} + etc + .... + ?YiYjYkYl (where all Y's are different) Finally E(YiYjYkYl) (where all Y's are different) = 0, since the Y's are independent with mean 0. 
January 25th, 2013, 03:55 AM  #5 
Senior Member Joined: Sep 2011 Posts: 140 Thanks: 0  Re: Statistics
Sorry but could you explain how the means are zero?


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