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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.
Independent: Each outcome of the die roll will not affect the next one, which means the 10 variables are independent from each other. Identically distributed: Regardless of whether the die is fair or weighted, each roll will have the same probability of seeing each result as every other roll. In contrast, rolling 10 different dice, some of ...
The best-fitting linear equation is often represented as a straight line to minimize the difference between the predicted values from the equation and the actual observed values of the dependent variable. Schematic of a scatterplot with simple line regression. Equation: = +: independent variable (predictor)
Pairwise independence does not imply mutual independence, as shown by the following example attributed to S. Bernstein. [3]Suppose X and Y are two independent tosses of a fair coin, where we designate 1 for heads and 0 for tails.
(That is, the two dice are independent.) If, however, the 1st die's result is a 3, and someone tells you about a third event - that the sum of the two results is even - then this extra unit of information restricts the options for the 2nd result to an odd number. In other words, two events can be independent, but NOT conditionally independent. [2]
If the first independent variable is a categorical variable (e.g. gender) and the second is a continuous variable (e.g. scores on the Satisfaction With Life Scale (SWLS)), then b 1 represents the difference in the dependent variable between males and females when life satisfaction is zero. However, a zero score on the Satisfaction With Life ...
In this example, the difference is nowhere near being normally distributed, since it has a substantial probability (about 0.88) of it being equal to 0. By contrast, the normal distribution, being a continuous distribution, has no discrete part—that is, it does not concentrate more than zero probability at any single point.