What expression represents the variance of a gamma distribution?

What expression represents the variance of a gamma distribution?

• A. αθ
• B. θα^2
• C. αθ^2
• D. α^2θ

Answer: (C)

To understand the variance of a gamma distribution, we need to recall the characteristics of this distribution. A gamma distribution is defined by two parameters: α (which is often referred to as the shape parameter) and θ (the scale parameter). The variance of the gamma distribution is calculated using the relationship between its parameters. The mathematical expression for the variance is given by the formula: Variance = αθ² This means that the variance is directly proportional to the shape parameter (α) and the square of the scale parameter (θ). Therefore, when looking for the expression that represents the variance of a gamma distribution, the correct formulation is αθ². This formulation arises from the properties of the gamma distribution, which reflects how the parameters affect the spread or dispersion of the distribution. Thus, the choice that includes α multiplied by θ squared accurately captures the variance of the gamma distribution, making it the correct answer.

To understand the variance of a gamma distribution, we need to recall the characteristics of this distribution. A gamma distribution is defined by two parameters: α (which is often referred to as the shape parameter) and θ (the scale parameter).

The variance of the gamma distribution is calculated using the relationship between its parameters. The mathematical expression for the variance is given by the formula:

Variance = αθ²

This means that the variance is directly proportional to the shape parameter (α) and the square of the scale parameter (θ). Therefore, when looking for the expression that represents the variance of a gamma distribution, the correct formulation is αθ².

This formulation arises from the properties of the gamma distribution, which reflects how the parameters affect the spread or dispersion of the distribution. Thus, the choice that includes α multiplied by θ squared accurately captures the variance of the gamma distribution, making it the correct answer.