Which of the following specifications could be used for a Normal distribution?

Which of the following specifications could be used for a Normal distribution?

• A. N(0, 0)
• B. N(1, 1)
• C. N(-1, -1)
• D. N(2, 4)

Answer: (B)

A Normal distribution is characterized by two parameters: the mean (µ) and the variance (σ²). The notation N(µ, σ²) specifies a Normal distribution where µ is the mean of the distribution and σ² is the variance. In this context, the option that is valid for a Normal distribution must have a positive variance because the variance reflects the spread of the distribution. If the variance is zero or negative, the distribution cannot exist since you can't have a spread that is either nonexistent or creates an invalid scenario. Looking specifically at the options, the specification N(1, 1) indicates a Normal distribution with a mean of 1 and a variance of 1. A variance of 1 is valid and provides a proper spread of the distribution, making this option suitable for describing a Normal distribution. Other options such as N(0, 0) would suggest a mean of 0 and a variance of 0, which results in a degenerate distribution that does not follow the characteristics of a Normal distribution. N(-1, -1) introduces a negative variance, which is not permissible, and N(2, 4) specifies a mean of 2 and variance of 4, which is valid but not selected as

A Normal distribution is characterized by two parameters: the mean (µ) and the variance (σ²). The notation N(µ, σ²) specifies a Normal distribution where µ is the mean of the distribution and σ² is the variance.

In this context, the option that is valid for a Normal distribution must have a positive variance because the variance reflects the spread of the distribution. If the variance is zero or negative, the distribution cannot exist since you can't have a spread that is either nonexistent or creates an invalid scenario.

Looking specifically at the options, the specification N(1, 1) indicates a Normal distribution with a mean of 1 and a variance of 1. A variance of 1 is valid and provides a proper spread of the distribution, making this option suitable for describing a Normal distribution.

Other options such as N(0, 0) would suggest a mean of 0 and a variance of 0, which results in a degenerate distribution that does not follow the characteristics of a Normal distribution. N(-1, -1) introduces a negative variance, which is not permissible, and N(2, 4) specifies a mean of 2 and variance of 4, which is valid but not selected as