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The mathematical model for probability has three major components: the sample space S, the family F of events, and the probability measure P (sometimes denoted Pr or Prob).
A probability model is a mathematical representation of a random phenomenon. It is defined by its sample space, events within the sample space, and probabilities associated with each event. The sample space S for a probability model is the set of all possible outcomes.
probability model: A drawing or chart used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. event: Any possible outcome of an experiment in probability.
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The main difference is that a probability model is only one (known) distribution, while a statistical model is a set of probability models; the data is used to select a model from this set or a smaller subset of models that better (in a certain sense) describe the phenomenon (in the light of the data).
In this lesson we'll learn about four specific types of probability models: the binomial distribution, the Poisson distribution, the normal distribution, and the bivariate normal distribution.
The main difference is that a probability model is only one (known) distribution, while a statistical model is a set of probability models; the data is used to select a model from this set or a smaller subset of models that better (in a certain sense) describe the phenomenon (in the light of the data).
The elementary probability model involves a sample space S of possible outcomes values, a class A={A} of events or subsets A of S that are of interest, and a probability P(A) for each event A.
There are three major types of probabilities: Theoretical Probability. Experimental Probability. Axiomatic Probability.

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