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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.
Therefore, in a formula, a dependent variable is a variable that is implicitly a function of another (or several other) variables. An independent variable is a variable that is not dependent. [19] The property of a variable to be dependent or independent depends often of the point of view and is not intrinsic.
Holding all other things constant is directly analogous to using a partial derivative in calculus rather than a total derivative, and to running a regression containing multiple variables rather than just one in order to isolate the individual effect of one of the variables. Ceteris paribus is an extension of scientific modeling.
An identity is an equality that is true for all values of its variables in a given domain. [18] An "equation" may sometimes mean an identity, but more often than not, it specifies a subset of the variable space to be the subset where the equation is true.
The relation not greater than can also be represented by , the symbol for "greater than" bisected by a slash, "not". The same is true for not less than, . The notation a ≠ b means that a is not equal to b; this inequation sometimes is considered a form of strict inequality. [4]
In that model, the random variables X 1, ..., X n are not independent, but they are conditionally independent given the value of p. In particular, if a large number of the X s are observed to be equal to 1, that would imply a high conditional probability , given that observation, that p is near 1, and thus a high conditional probability , given ...
The variable y is directly proportional to the variable x with proportionality constant ~0.6. The variable y is inversely proportional to the variable x with proportionality constant 1. In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.
To be precise, what is sought are often not necessarily actual values, but, more in general, expressions. A solution of the inequation is an assignment of expressions to the unknowns that satisfies the inequation(s); in other words, expressions such that, when they are substituted for the unknowns, make the inequations true propositions.