Proof of strong law of large number

  • Thread starter Thread starter Darkzo-n
  • Start date Start date
  • Tags Tags
    Law Proof
Darkzo-n
Messages
1
Reaction score
0
Hi, i had recently come across the proof of the strong law of large number.
Inside the proof , it assumed the random variable have a finite fourth moment. may i know y is the assumption necessary and why the 4th? why not 2nd or 3rd or 5th?
 
Physics news on Phys.org
Hey Darkzo-n and welcome to the forums.

For this problem, the kurtosis is defined as the expectation of [(X - mu)/sigma]^4.

If the distribution has an infinite mean in either direction, then the kurtosis will not exist. If the mean is zero, then X - mu will also be zero as well so that's not an issue.

The gaurantee of a mean of some sort is what makes the Strong law have its power because things converge to some mean, and without this finite quality, the convergence can not take place and the thing won't work.
 

Thread 'Here's a Statistics problem for game of Polo (or Hockey if you like)'

Namaste & G'day Postulate: A strongly-knit team wins on average over a less knit one Fundamentals: - Two teams face off with 4 players each - A polo team consists of players that each have assigned to them a measure of their ability (called a "Handicap" - 10 is highest, -2 lowest) I attempted to measure close-knitness of a team in terms of standard deviation (SD) of handicaps of the players. Failure: It turns out that, more often than, a team with a higher SD wins. In my language, that...
View full post »

Thread 'Roulette wheel physics and probability'

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
View full post »

Similar threads

I Understanding extinction probability in simple GWP
Replies
1
Views
2K
(weak) Law of Large Numbers and variance
Replies
14
Views
6K
I Understanding different Monte Carlo approximation notations
Replies
7
Views
2K
What is the difference between weak and strong large number laws?
Replies
1
Views
5K
Gambling and the law of large numbers
Replies
8
Views
7K
I Proof that BB(k) grows faster than any computable function
Replies
15
Views
6K
Strong law of large numbers - help understanding it
Replies
2
Views
3K
I Snell's law from a mechanical model
Replies
12
Views
2K
Admissions Direct Entry to PhD Program -- Advice Please
Replies
36
Views
4K
Chemistry Show that book levitation by absorption of heat violates 2nd law
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top