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In essence probability is influenced by a person's information about the possible occurrence of an event. For example, let the event A {\displaystyle A} be 'I have a new phone'; event B {\displaystyle B} be 'I have a new watch'; and event C {\displaystyle C} be 'I am happy'; and suppose that having either a new phone or a new watch increases ...
In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. . Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
Seen as a function of for given , (= | =) is a probability mass function and so the sum over all (or integral if it is a conditional probability density) is 1. Seen as a function of x {\displaystyle x} for given y {\displaystyle y} , it is a likelihood function , so that the sum (or integral) over all x {\displaystyle x} need not be 1.
Given two events A and B from the sigma-field of a probability space, with the unconditional probability of B being greater than zero (i.e., P(B) > 0), the conditional probability of A given B (()) is the probability of A occurring if B has or is assumed to have happened. [5]
In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events , hence the name.
In probability theory, an event is a subset of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
The dependent variable is the event expected to change when the independent variable is manipulated. [ 11 ] In data mining tools (for multivariate statistics and machine learning ), the dependent variable is assigned a role as target variable (or in some tools as label attribute ), while an independent variable may be assigned a role as regular ...
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