# Réponse finale obtenue du bot:
response = « A fascinating topic! Let’s dive into the properties of statistical and probabilistic concepts, exploring the theories and applications that underlie them.
**Théorie des probabilités**
1. **Fundamental Theorem of Probability**: The probability of an event is equal to the number of favorable outcomes divided by the total number of possible outcomes.
2. **Additivity**: The probability of the union of two or more events is equal to the sum of their individual probabilities, minus the probability of their intersection.
**Statistiques descriptives et inférentielles**
1. **Descriptive Statistics**: Measures that summarize and describe the main features of a dataset, such as mean, median, mode, range, variance, and standard deviation.
2. **Inferential Statistics**: Methods used to draw conclusions about a population based on a sample of data from that population.
**Modèles stochastiques**
1. **Random Processes**: Models that describe the behavior of random phenomena over time or space, such as Brownian motion, Gaussian processes, and Markov chains.
2. **Stochastic Differential Equations (SDEs)**: Equations that describe the evolution of a system over time, with randomness introduced through stochastic integrals.
**Other Properties**
1. **Law of Large Numbers**: As the sample size increases, the average value of a random variable will converge to its expected value.
2. **Central Limit Theorem**: The distribution of the mean of a large number of independent and identically distributed random variables will approach a normal distribution, regardless of the underlying distribution.
These properties form the foundation of statistical and probabilistic reasoning, enabling us to analyze data, make predictions, and understand complex systems.
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