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In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]
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.
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
The independent variables are mentioned in the list of arguments that the function takes, whereas the parameters are not. For example, in the logarithmic function f ( x ) = log b ( x ) , {\displaystyle f(x)=\log _{b}(x),} the base b {\displaystyle b} is considered a parameter.
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
The definition extends naturally to more than two random variables. We say that random variables , …, are i.i.d. if they are independent (see further Independence (probability theory) § More than two random variables) and identically distributed, i.e. if and only if
Suppose X and Y are two independent tosses of a fair coin, where we designate 1 for heads and 0 for tails. Let the third random variable Z be equal to 1 if exactly one of those coin tosses resulted in "heads", and 0 otherwise (i.e., Z = X ⊕ Y {\displaystyle Z=X\oplus Y} ).
The variables made to remain constant during an experiment are referred to as control variables. For example, if an outdoor experiment were to be conducted to compare how different wing designs of a paper airplane (the independent variable) affect how far it can fly (the dependent variable), one would want to ensure that the experiment is ...