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Stochastic independence implies mean independence, but the converse is not true.; [1] [2] moreover, mean independence implies uncorrelatedness while the converse is not true. Unlike stochastic independence and uncorrelatedness, mean independence is not symmetric: it is possible for Y {\displaystyle Y} to be mean-independent of X {\displaystyle ...
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 ...
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.
A random sample can be thought of as a set of objects that are chosen randomly. More formally, it is "a sequence of independent, identically distributed (IID) random data points." In other words, the terms random sample and IID are synonymous. In statistics, "random sample" is the typical terminology, but in probability, it is more common to ...
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 ...
Further, two jointly normally distributed random variables are independent if they are uncorrelated, [4] although this does not hold for variables whose marginal distributions are normal and uncorrelated but whose joint distribution is not joint normal (see Normally distributed and uncorrelated does not imply independent).
In statistics and social sciences, an antecedent variable is a variable that cannot help to explain the apparent relationship (or part of the relationship) between other variables that are nominally in a cause and effect relationship.