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January 13th, 2013, 08:13 PM   #1
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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
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January 14th, 2013, 01:55 PM   #2
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Re: Statistics

It is simply a multinomial expansion. The terms where all the X's are different get canceled by the mean.
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January 14th, 2013, 03:12 PM   #3
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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?
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January 15th, 2013, 01:05 PM   #4
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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.
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January 25th, 2013, 03:55 AM   #5
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Re: Statistics

Sorry but could you explain how the means are zero?
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