Suppose let be i.i.d. with N(1,3) random variables. How can I show that:

(a.s)

From my understanding:

Then the nominator will go to 1.. How about the denominator? Why is its expected value 4?

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- October 30th 2010, 06:26 AMnoob mathematicianStrong law of large number
Suppose let be i.i.d. with N(1,3) random variables. How can I show that:

(a.s)

From my understanding:

Then the nominator will go to 1.. How about the denominator? Why is its expected value 4? - October 31st 2010, 03:16 AMMoo
Hello,

It's not exactly the numerator that will go to 1, but it's

You have

For the second term, we know - also from the SLLN, that it tends to . But we know that , so the result should be...