Final answer:
The variance function of white noise with unit variance is constant and equal to 1, denoted as σ² = 1.
Step-by-step explanation:
In probability theory and statistics, white noise is a random signal with constant variance and zero autocorrelation at any lag. When white noise has a unit variance, it means that the variance of the noise remains constant and is equal to 1. Variance, denoted as σ², measures the variability or dispersion of a set of values from their mean. In the case of white noise with unit variance, this value remains consistent over time or any given set of observations.
The variance function defines how the variance of a random variable changes with different inputs. In the context of white noise, the variance function is simple and constant. Mathematically, if σ² represents the variance, when it's specified as having unit variance, it implies that σ² = 1. This means that the variance remains constant and doesn't depend on any input or time index, signifying the constant and stable nature of the noise process.
The constant variance of 1 for white noise indicates that the variability around the mean value remains the same throughout observations or time intervals. This property is fundamental in various fields, including signal processing, where white noise with unit variance is commonly used as a model for random fluctuations or disturbances in a system, providing a baseline for analyzing and understanding noise characteristics.