# Réponse finale obtenue du bot:
response = « A fascinating topic!
Let’s dive into the properties of probability and statistics:
**Theory of Probability**
1. **Fundamental Theorem of Probability**: The probability of an event is equal to the sum of the probabilities of all possible outcomes.
2. **Additivity**: The probability of a union of two events is equal to the sum of their individual probabilities minus the probability of their intersection.
3. **Commutativity**: The order in which we perform operations on events does not affect the result.
**Descriptive Statistics**
1. **Mean**: A measure of central tendency, calculated by averaging all values.
2. **Median**: A value that separates the higher half from the lower half of a dataset, often used when data is skewed or has outliers.
3. **Mode**: The most frequently occurring value in a dataset.
**Inferential Statistics**
1. **Sampling Distribution**: The distribution of statistics (e.g., mean, proportion) calculated from multiple samples.
2. **Confidence Interval**: A range within which the true population parameter is likely to lie, based on sample data.
3. **Hypothesis Testing**: Statistical procedures used to determine whether a hypothesis about a population parameter is supported by sample data.
**Stochastic Models**
1. **Random Variables**: Mathematical functions that assign a numerical value to each possible outcome of an experiment.
2. **Probability Distributions**: Functions that describe the probability of different outcomes, such as normal, binomial, or Poisson distributions.
3. **Markov Chains**: Mathematical models used to analyze systems that undergo transitions from one state to another based on certain probabilities.
These are just a few examples of the properties and concepts in probability and statistics. If you’d like me to elaborate on any specific topic or provide more information, feel free to ask! »