haruspex said:Looks ok to me.
mathman said:If you want something more interesting, you can work with discrete sets. Example: 2 elements (A,B) with P(A) = 1/3 and P(B) = 2/3.
A probability space is a mathematical framework used to model and analyze random events or processes. It consists of a sample space, a set of all possible outcomes, and a probability measure that assigns a numerical value to each outcome.
A probability space is constructed by defining a sample space and a probability measure. The sample space can be discrete, such as a set of numbers, or continuous, such as an interval on the number line. The probability measure assigns a probability to each element in the sample space, ensuring that the sum of all probabilities is equal to 1.
A probability space is a mathematical framework, while a probability distribution is a function that describes the probabilities of possible outcomes. A probability distribution can be constructed using a probability space, but they are not the same thing.
Constructing a probability space allows us to mathematically model and analyze random events or processes. It provides a framework for understanding the likelihood of different outcomes and can help us make informed decisions or predictions based on probability.
Probability spaces are used in a wide range of fields, including physics, finance, and statistics. Some examples of real-world applications include predicting stock market fluctuations, analyzing the risk of natural disasters, and understanding the spread of diseases.