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The probability of drawing a red ball from either of the urns is 2 / 3 , and the probability of drawing a blue ball is 1 / 3 . The joint probability distribution is presented in the following table:
It is constructed from the joint probability distribution of the random variable that (presumably) ... One example occurs in 2×2 tables, ...
In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables).
When both and are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable.
In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
The conditional probability can be found by the quotient of the probability of the joint intersection of events A and B, that is, (), the probability at which A and B occur together, and the probability of B: [2] [6] [7] = ().
For two discrete random variables, it is beneficial to generate a table of probabilities and address the cumulative probability for each potential range of X and Y, and here is the example: [10] given the joint probability mass function in tabular form, determine the joint cumulative distribution function.
Using a Bayesian network can save considerable amounts of memory over exhaustive probability tables, if the dependencies in the joint distribution are sparse. For example, a naive way of storing the conditional probabilities of 10 two-valued variables as a table requires storage space for 2 10 = 1024 {\displaystyle 2^{10}=1024} values.