Question

The standard normal distribution is a

• A. non-parametric distribution.
• B. single parameter distribution.
• C. two-parameter distribution.
• D. three-parameter distribution.

Hint:

Normal distributions are always defined by mean and variance; fixing them does not reduce the parameter count.

Answer 1

The Correct Option is C

The normal distribution is a continuous probability distribution described by the parameters: - the mean \( \mu \), which determines the central tendency,
- the variance \( \sigma^2 \), which determines the spread.
The general probability density function (PDF) is: \[ f(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left( -\frac{(x - \mu)^2}{2\sigma^2} \right), \] which clearly shows dependence on both parameters. The standard normal distribution is a special case where: \[ \mu = 0, \sigma = 1. \] Even though these values are fixed, the distribution remains part of the two-parameter family. It is incorrect to label the standard version as a single-parameter or non-parametric distribution because its structure is inherently tied to the two parameters that define the normal family. Therefore, from the viewpoint of statistical classification, normal distributions—including the standard normal—are always two-parameter distributions. Hence option (C) is correct.