Difference between simple probability and marginal probability
Answers
simple prob
The ratio of the number of outcomes favourable for the event to the total number of possible outcomes is termed as probability. In other words, a measure of the likelihood of an event (or measure of chance) is called probability. The basic terms involved in probability are listed below:
Experiment is one of several possible outcomes that are obtained from any process.
Sample space is the possible outcomes of the experiment.
Events are the subsets of the sample space.
marginal prob
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Probability theory
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Probability axioms
Probability space Sample space Elementary event Event Random variable Probability measure
Complementary event Joint probability Marginal probability Conditional probability
Independence Conditional independence Law of total probability Law of large numbers Bayes' theorem Boole's inequality
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vte
In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables.
Marginal variables are those variables in the subset of variables being retained. These concepts are "marginal" because they can be found by summing values in a table along rows or columns, and writing the sum in the margins of the table.[1] The distribution of the marginal variables (the marginal distribution) is obtained by marginalizing – that is, focusing on the sums in the margin – over the distribution of the variables being discarded, and the discarded variables are said to have been marginalized out.
The context here is that the theoretical studies being undertaken, or the data analysis being done, involves a wider set of random variables but that attention is being limited to a reduced number of those variables. In many applications, an analysis may start with a given collection of random variables, then first extend the set by defining new ones (such as the sum of the original random variables) and finally reduce the number by placing interest in the marginal distribution of a subset (such as the sum). Several different analyses may be done, each treating a different subset of variables as the marginal variables.