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Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.
¯ = sample mean of differences d 0 {\displaystyle d_{0}} = hypothesized population mean difference s d {\displaystyle s_{d}} = standard deviation of differences
Over a variable name, means that the variable represents a vector, in a context where ordinary variables represent scalars; for example, . Boldface ( v {\displaystyle \mathbf {v} } ) or a circumflex ( v ^ {\displaystyle {\hat {v}}} ) are often used for the same purpose.
In physics, the names of variables are largely determined by the physical quantity they describe, but various naming conventions exist. A convention often followed in probability and statistics is to use X, Y, Z for the names of random variables, keeping x, y, z for variables representing corresponding better-defined values.
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 ...
Values of each variable statistically "vary" (or are distributed) across the variable's domain. A domain is a set of all possible values that a variable is allowed to have. The values are ordered in a logical way and must be defined for each variable. Domains can be bigger or smaller.
the population mean or expected value in probability and statistics; a measure in measure theory; micro-, an SI prefix denoting 10 −6 (one millionth) Micrometre or micron (retired in 1967 as a standalone symbol, replaced by "μm" using the standard SI meaning) the coefficient of friction in physics; the service rate in queueing theory
If the random variable is denoted by , then the mean is also known as the expected value of (denoted ()). For a discrete probability distribution , the mean is given by ∑ x P ( x ) {\displaystyle \textstyle \sum xP(x)} , where the sum is taken over all possible values of the random variable and P ( x ) {\displaystyle P(x)} is the probability ...