Strong Law of Large Numbers imply Weak Law [closed]
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If the Strong Law of Large Numbers imply the Weak Law, why do we have a Weak Law of Large Numbers?
probability measure-theory random-variables law-of-large-numbers
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
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closed as unclear what you're asking by amWhy, Shailesh, Kavi Rama Murthy, user593746, BigbearZzz Dec 15 '18 at 17:18
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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If the Strong Law of Large Numbers imply the Weak Law, why do we have a Weak Law of Large Numbers?
probability measure-theory random-variables law-of-large-numbers
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
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closed as unclear what you're asking by amWhy, Shailesh, Kavi Rama Murthy, user593746, BigbearZzz Dec 15 '18 at 17:18
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
3
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Because the weak law does not imply the strong law.
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– drhab
Dec 15 '18 at 12:14
1
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And because we have several types of convergence in probability theory
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– Fakemistake
Dec 15 '18 at 12:54
add a comment |
$begingroup$
If the Strong Law of Large Numbers imply the Weak Law, why do we have a Weak Law of Large Numbers?
probability measure-theory random-variables law-of-large-numbers
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
$endgroup$
If the Strong Law of Large Numbers imply the Weak Law, why do we have a Weak Law of Large Numbers?
probability measure-theory random-variables law-of-large-numbers
probability measure-theory random-variables law-of-large-numbers
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
edited Dec 15 '18 at 12:13
mrtaurho
4,61621235
4,61621235
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
asked Dec 15 '18 at 12:07
Sudheesh SurendranathSudheesh Surendranath
18718
18718
closed as unclear what you're asking by amWhy, Shailesh, Kavi Rama Murthy, user593746, BigbearZzz Dec 15 '18 at 17:18
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by amWhy, Shailesh, Kavi Rama Murthy, user593746, BigbearZzz Dec 15 '18 at 17:18
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
3
$begingroup$
Because the weak law does not imply the strong law.
$endgroup$
– drhab
Dec 15 '18 at 12:14
1
$begingroup$
And because we have several types of convergence in probability theory
$endgroup$
– Fakemistake
Dec 15 '18 at 12:54
add a comment |
3
$begingroup$
Because the weak law does not imply the strong law.
$endgroup$
– drhab
Dec 15 '18 at 12:14
1
$begingroup$
And because we have several types of convergence in probability theory
$endgroup$
– Fakemistake
Dec 15 '18 at 12:54
3
3
$begingroup$
Because the weak law does not imply the strong law.
$endgroup$
– drhab
Dec 15 '18 at 12:14
$begingroup$
Because the weak law does not imply the strong law.
$endgroup$
– drhab
Dec 15 '18 at 12:14
1
1
$begingroup$
And because we have several types of convergence in probability theory
$endgroup$
– Fakemistake
Dec 15 '18 at 12:54
$begingroup$
And because we have several types of convergence in probability theory
$endgroup$
– Fakemistake
Dec 15 '18 at 12:54
add a comment |
1 Answer
1
active
oldest
votes
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A weak law may come with some estimate of the rate of convergence which is not available for the strong law. In practical situations, such as statistics, you never have a whole infinite sequence of trials, only a finite sequence. Yet you would still like to deduce something about the underlying probability distribution.
The textbook
Chung, Kai Lai, Elementary probability theory with stochastic processes, Undergraduate Texts in Mathematics. New York - Heidelberg - Berlin: Springer-Verlag. X, 325 p. Cloth DM 29.40; $ 12.00 (1974). ZBL0293.60001.
perplexes students by showing two quotes on the same page, one saying that the strong law is superior to the weak, and the other saying the weak law is superior to the strong. This leaves the poor instructor (me) to explain the discrepancy!
Here it is, from page 233 in the first edition:
Feller: "[the weak law of large numbers] is of very limited interest and hould be replaced by the more precise and more useful strong law of large numbers" (p. 152 of An Introduction to Probability Theory and its Applications, vol I, 3rd edition, 1971).
van der Waerden: "[the strong law of large numbers] scarcely plays a role in mathematical statistics" (p. 98 of Mathematische Statistik, 3rd ed, 1971)
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
A weak law may come with some estimate of the rate of convergence which is not available for the strong law. In practical situations, such as statistics, you never have a whole infinite sequence of trials, only a finite sequence. Yet you would still like to deduce something about the underlying probability distribution.
The textbook
Chung, Kai Lai, Elementary probability theory with stochastic processes, Undergraduate Texts in Mathematics. New York - Heidelberg - Berlin: Springer-Verlag. X, 325 p. Cloth DM 29.40; $ 12.00 (1974). ZBL0293.60001.
perplexes students by showing two quotes on the same page, one saying that the strong law is superior to the weak, and the other saying the weak law is superior to the strong. This leaves the poor instructor (me) to explain the discrepancy!
Here it is, from page 233 in the first edition:
Feller: "[the weak law of large numbers] is of very limited interest and hould be replaced by the more precise and more useful strong law of large numbers" (p. 152 of An Introduction to Probability Theory and its Applications, vol I, 3rd edition, 1971).
van der Waerden: "[the strong law of large numbers] scarcely plays a role in mathematical statistics" (p. 98 of Mathematische Statistik, 3rd ed, 1971)
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
$endgroup$
add a comment |
$begingroup$
A weak law may come with some estimate of the rate of convergence which is not available for the strong law. In practical situations, such as statistics, you never have a whole infinite sequence of trials, only a finite sequence. Yet you would still like to deduce something about the underlying probability distribution.
The textbook
Chung, Kai Lai, Elementary probability theory with stochastic processes, Undergraduate Texts in Mathematics. New York - Heidelberg - Berlin: Springer-Verlag. X, 325 p. Cloth DM 29.40; $ 12.00 (1974). ZBL0293.60001.
perplexes students by showing two quotes on the same page, one saying that the strong law is superior to the weak, and the other saying the weak law is superior to the strong. This leaves the poor instructor (me) to explain the discrepancy!
Here it is, from page 233 in the first edition:
Feller: "[the weak law of large numbers] is of very limited interest and hould be replaced by the more precise and more useful strong law of large numbers" (p. 152 of An Introduction to Probability Theory and its Applications, vol I, 3rd edition, 1971).
van der Waerden: "[the strong law of large numbers] scarcely plays a role in mathematical statistics" (p. 98 of Mathematische Statistik, 3rd ed, 1971)
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
$endgroup$
add a comment |
$begingroup$
A weak law may come with some estimate of the rate of convergence which is not available for the strong law. In practical situations, such as statistics, you never have a whole infinite sequence of trials, only a finite sequence. Yet you would still like to deduce something about the underlying probability distribution.
The textbook
Chung, Kai Lai, Elementary probability theory with stochastic processes, Undergraduate Texts in Mathematics. New York - Heidelberg - Berlin: Springer-Verlag. X, 325 p. Cloth DM 29.40; $ 12.00 (1974). ZBL0293.60001.
perplexes students by showing two quotes on the same page, one saying that the strong law is superior to the weak, and the other saying the weak law is superior to the strong. This leaves the poor instructor (me) to explain the discrepancy!
Here it is, from page 233 in the first edition:
Feller: "[the weak law of large numbers] is of very limited interest and hould be replaced by the more precise and more useful strong law of large numbers" (p. 152 of An Introduction to Probability Theory and its Applications, vol I, 3rd edition, 1971).
van der Waerden: "[the strong law of large numbers] scarcely plays a role in mathematical statistics" (p. 98 of Mathematische Statistik, 3rd ed, 1971)
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
$endgroup$
A weak law may come with some estimate of the rate of convergence which is not available for the strong law. In practical situations, such as statistics, you never have a whole infinite sequence of trials, only a finite sequence. Yet you would still like to deduce something about the underlying probability distribution.
The textbook
Chung, Kai Lai, Elementary probability theory with stochastic processes, Undergraduate Texts in Mathematics. New York - Heidelberg - Berlin: Springer-Verlag. X, 325 p. Cloth DM 29.40; $ 12.00 (1974). ZBL0293.60001.
perplexes students by showing two quotes on the same page, one saying that the strong law is superior to the weak, and the other saying the weak law is superior to the strong. This leaves the poor instructor (me) to explain the discrepancy!
Here it is, from page 233 in the first edition:
Feller: "[the weak law of large numbers] is of very limited interest and hould be replaced by the more precise and more useful strong law of large numbers" (p. 152 of An Introduction to Probability Theory and its Applications, vol I, 3rd edition, 1971).
van der Waerden: "[the strong law of large numbers] scarcely plays a role in mathematical statistics" (p. 98 of Mathematische Statistik, 3rd ed, 1971)
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
edited Dec 15 '18 at 15:40
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
answered Dec 15 '18 at 15:30
GEdgarGEdgar
62.5k267171
62.5k267171
add a comment |
add a comment |
3
$begingroup$
Because the weak law does not imply the strong law.
$endgroup$
– drhab
Dec 15 '18 at 12:14
1
$begingroup$
And because we have several types of convergence in probability theory
$endgroup$
– Fakemistake
Dec 15 '18 at 12:54