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