The document discusses the law of large numbers, which states that as the number of trials or observations increases, the empirical probability or sample average will get closer to the actual or theoretical probability. It provides examples of flipping a coin and money in a wallet. The history of the concept is explored from its foundations with Cardano and Bernoulli to its naming by Poisson. Applications discussed include roulette odds stabilizing with more spins, Tesla's growth rates changing as it scales up, and its use in insurance risk calculation. Overcoming the challenges for large companies is also mentioned.

1. Law of Large
number
Group 5

2. This is our
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3. What we'll discuss ?
- Definition and illustration of Law
of Large Number.
- History of Law of Large
Number.
- Some Applications in Game,
Business and Insurance.
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4. Group 5
Definition
and
Illustration

5. "An unknow Proportion
can reach a degree of
accurancy through an
appropriate number of
trials "
- Jacob Bernoulli -
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6. The number of trials or observations increases,
the empirical probability will get closer and
closer to the actual or the theoretical
probability of the event.
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7. The number of trials or observations increases,
the empirical probability will get closer and
closer to the actual or the theoretical
probability of the event
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8. Empirical probability
Theoretical probability
Experimental probability
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9. Empirical probability: basically relative
frequency for an experiment or in a
simulation that you may do
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10. Theoretical probability is based on
what is expected to happen, or a
theory, using reasoning.
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11. Experimental probability is
based on what actually occurs
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12. Let's flip a coin!
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13. The theoretical probability of
flipping heads and tails is 50%
Experiment 1: Flipping 10 times
Experiment 2: Flipping 100 time
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14. 5 10 15
0.75
0.5
0.25
0
Cumulative
proportion
of
head
Number of Flip
Theoretical
probability

15. How much money do you
have in your wallet ?

16. 49 39
47

17. An observed sample average
from a large sample will be close
to the true population average
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18. A small sample will reflect the true
population characteristics
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19. The law of large numbers indicates a
bigger sample will represent a
population mean
The central tendency theorem states
a bigger sample will represent a
population's distribution
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20. Strong form of Law of Large Number

21. Weak form of Law of Large Number

22. History of
Law of Large Number
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23. SiméonDenisPoisson
JacobBernoulli
1501 - 1575 1837
1713
GerolamoCardano
1867
PafnutyChebyshev
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24. 1501 - 1575
GerolamoCardano
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He found that as more trials are conducted, the
result will become closer to the desired result.
But he can't proved it!
This is the foundation of the Law of Large
number.

25. JacobBernoulli
1713
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He proved the Law of Large number in 1713
It took him 20 years to develop a sufficiently
rigorous mathematical proof
It became generally known as "Bernoulli's theorem"

26. SiméonDenisPoisson
1837
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The name "The law of large numbers" was
coined in 1837 by the French
mathematician, Siméon Denis Poisson

27. 1867
PafnutyChebyshev
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There is also a more general version of the
law of large numbers for averages, proved
more than a century later by the Russian
mathematician Pafnuty Chebyshev

28. Group 5
Some Applications in
Game, Business and Insurance.

29. Group 5
The game of Roulette

30. Group 5
The game of Roulette

31. Group 5
37 number: 0 - 36
Zero : green
18 number in red boxes
18 number in black boxes

32. Group 5
It has one more 00 green box
--> The advantage of bookmaker will be
higher

33. Group 5
Rules:
Bet$1inredboxes-->win$1
Iftheballlandinblackorgreen
boxes--> lose$2

34. In Business

35. In 2020: $24.604 billions.
Increase of roughly 79%
The law indicates that as
Tesla continues to grow !

36. - The relationship between scale and growth
rates.
- As a company becomes bigger, it will experience
difficulties maintaining percentage targets.
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37. Group 5
In Insurance

38. Group5
It prominent in the insurance industry to
calculate and refine projected risk!

39. In Business?
The important of the Law of Large Number
In Statistical analysis?

40. The law of large
numbers is important
because it gives value
to your sample.
In Statistical analysis?

41. In Business?
The law of large
numbers is important
when setting targets
or goals!

42. HowcanCompamiesovercomethechallenge
of LawofLargeNumber?

43. - Companies often acquiring smaller growth companies that
can infuse scalable growth.
- They also attempt to become more efficient and utilize
their size for manufacturing, ordering, or distribution
benefits.
- Last, companies can be more attentive to dollar goals as
opposed to percent goals.

44. Thank you for
your listening!