standard normal random variable meaning: definition, quotations

standard normal random variable

noun

Mathematics, Probability theory, Sciences, Statistics A random variable whose probability distribution is a standard normal distribution.

Suppose X#92;simN(#92;mu,#92;sigma). Then Z#61;#92;frac#123;x-#92;mu#125;#123;#92;sigma#125; is a standard normal random variable. In other words, any normal random variable can be standardized by subtracting the mean from the variable and dividing the difference by the standard deviation.2000, George E. Monahan, Management Decision Making: Spreadsheet modeling, analysis, and applications, volume 1, Cambridge University Press, page 405:
This technique is based on a polynomial transformation that proceeds by taking the sum of a linear combination of a standard normal random variable, its square, and its cube.2010, Todd C. Headrick, Statistical Simulation: Power Method Polynomials and Other Transformations, Taylor & Francis (CRC Press), page 1:

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2016, Maria Dolores Ugarte, Ana F. Militino, Alan T. Arnholt, Probability and Statistics with R, 2nd Edition, Taylor & Francis (CRC Press), page 297, A normal random variable with μ = 0 and σ = 1, often denoted Z, is called a standard normal random variable. […] Further, any normal random variable can be converted to a standard normal random variable using (4.25).