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Treball de fi de grau

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cc-by-nc-nd (c) Aina Nadal Gavaldà, 2024
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/211580

From probability to convergence: exploring the foundations of the central limit theorem

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[en] This thesis embarks on a mathematical journey, delving into the depths of probability theory and a comprehensive exploration of the Central Limit Theorem (CLT). The study begins with fundamental concepts such as characteristic functions and basic probability theory, continuing with the laws of large numbers. Afterwards, the narrative progresses to focus on various versions of the CLT. Essential theorems, including De Moivre-Laplace’s, Lindeberg-Lévy’s, and Lyapunov’s, are studied, offering insights into the universal significance of the CLT. The journey concludes with a glimpse of the constraints of this impactful theorem, including the convergence of the compound Poisson distribution. This work contributes to a nuanced understanding of probability theory as well as serves as a guide through the elegance and applicability of the CLT.

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: David Márquez

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NADAL GAVALDÀ, Aina. From probability to convergence: exploring the foundations of the central limit theorem. [consulta: 27 de gener de 2026]. [Disponible a: https://hdl.handle.net/2445/211580]

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