משפט הגבול המרכזי. אופק • צפה בנושא

} Distributions Ξ which can arise in this way are called Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability: 583—602
Topological Crystallography — With a View Towards Discrete Geometric Analysis ישנם מקרים מעשיים רבים כוללים דגימה ללא החזרה למשל ביצור שם דוגמים במסגרת בקרת איכות פריטים מסדרה מסדרת מוצרים סופית מבלי להחליף אותם

If this procedure is performed many times, the central limit theorem says that the of the average will closely approximate a normal distribution.

חוק המספרים הגדולים
Information Theory and the Central Limit Theorem
אופק • צפה בנושא
The law would have been personified by the Greeks and deified, if they had known of it
חוק המספרים הגדולים
Formally, the theorem can be stated as follows: Lindeberg—Lévy CLT
The same also holds in all dimensions greater than 2 הוכחת גרסה זו מסובכת יותר
If a sequence of random variables satisfies Lyapunov's condition, then it also satisfies Lindeberg's condition Bernstein presents a historical discussion focusing on the work of and his students and that led to the first proofs of the CLT in a general setting

The actual term "central limit theorem" in German: "zentraler Grenzwertsatz" was first used by in 1920 in the title of a paper.

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אופק • צפה בנושא
Central limit theorem
The multidimensional central limit theorem states that when scaled, sums converge to a
Central limit theorem
} The rate of convergence is given by the following type result: Theorem
A Survey and Some Open Questions" בתורת ההסתברות חוק המספרים הגדולים בעצם מפרמל את העובדה הפשוטה, שכשממצעים מספיק דגימות ההתפלגות תהיה בערך כמו התוחלת
The central limit theorem has several variants Applied Statistics and Probability for Engineers 6th ed

Heber City, UT: Kendrick Press.

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משפט הגבול המרכזי
In variants, convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, if they comply with certain conditions
חוק המספרים הגדולים
Using generalisations of the central limit theorem, we can then see that this would often though not always produce a final distribution that is approximately normal
חוק המספרים הגדולים
Informally, something along these lines happens when the sum, S n, of independent identically distributed random variables, X 1, …, X n, is studied in classical probability theory