# Réponse finale obtenue du bot:
response = « Here’s an exploration of the properties of probability and statistics:
**Theory of Probability**
1. **Commutativity**: The order in which events are combined does not affect the result.
2. **Associativity**: The combination of events can be performed in any order without affecting the result.
3. **Distributivity**: The probability of a union or intersection of two events is equal to the sum or product, respectively, of their individual probabilities.
4. **Additivity**: The probability of a union of multiple events is equal to the sum of their individual probabilities.
**Descriptive Statistics**
1. **Mean**: The average value of a set of data.
2. **Median**: The middle value of a set of data when it’s arranged in order.
3. **Mode**: The most frequently occurring value in a set of data.
4. **Range**: The difference between the largest and smallest values in a set of data.
**Inferential Statistics**
1. **Sample Mean**: An estimate of the population mean based on a random sample from the population.
2. **Sample Proportion**: An estimate of the population proportion based on a random sample from the population.
3. **Confidence Interval**: A range within which we can be confident that the true value lies, with a certain level of confidence.
4. **Hypothesis Testing**: A method to test a hypothesis about a population parameter based on a sample statistic.
**Stochastic Models**
1. **Random Variables**: Variables whose values are determined by chance.
2. **Probability Distributions**: Functions that describe the probability of different outcomes of a random variable.
3. **Expectation**: The long-term average value of a random variable.
4. **Variance**: A measure of how spread out the values of a random variable are.
These are just some of the key properties and concepts in statistics and probability. I hope this helps! »