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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 be 'I have a new phone'; event be 'I have a new watch'; and event be 'I am happy'; and suppose that having either a new phone or a new watch increases the probability of my being happy.
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.
In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) [2] or occasionally P B (A).
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.
Then the unconditional probability that = is 3/6 = 1/2 (since there are six possible rolls of the dice, of which three are even), whereas the probability that = conditional on = is 1/3 (since there are three possible prime number rolls—2, 3, and 5—of which one is even).
While the number of independent random events grows, the related joint probability value decreases rapidly to zero, according to a negative exponential law. Similarly, two absolutely continuous random variables are independent if and only if , (,) = ()
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 ...