standard normal random variable

English

Noun

standard normal random variable (plural standard normal random variables)

1. (probability theory, statistics) A random variable whose probability distribution is a standard normal distribution.
   • 2000, George E. Monahan, Management Decision Making: Spreadsheet modeling, analysis, and applications, volume 1, Cambridge University Press, page 405:

     Suppose $X\sim N(\mu ,\sigma )$. Then
     $Z={\frac {x-\mu }{\sigma }}$
     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.

   • 2010, Todd C. Headrick, Statistical Simulation: Power Method Polynomials and Other Transformations‎^[1], Taylor & Francis (CRC Press), page 1:

     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.

   • 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).

Synonyms

• (random variable): standard normal variable

Related terms

• standard normal deviate