Meaning of standard normal random variable | Babel Free

Definitions

A random variable whose probability distribution is a standard normal distribution.

Examples

“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.”

“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).”

CEFR level