What is the variance of an exponential distribution?

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What is the variance of an exponential distribution?

To find the variance of an exponential distribution, it is essential to understand its parameters. The exponential distribution is defined by its rate parameter, often denoted as λ (lambda), which is the inverse of the scale parameter θ (theta), where θ = 1/λ. The variance of an exponential distribution is calculated using the formula: Variance = θ² This highlights that the variance is directly dependent on the square of the scale parameter. Since θ represents the average time until an event occurs, the square of this parameter provides insight into the spread of the distribution. Given this understanding, θ² stands out as the correct answer regarding the variance of an exponential distribution. It accurately represents the relationship between the variance and the scale of the distribution, aligning with the properties of exponential random variables.

To find the variance of an exponential distribution, it is essential to understand its parameters. The exponential distribution is defined by its rate parameter, often denoted as λ (lambda), which is the inverse of the scale parameter θ (theta), where θ = 1/λ.

The variance of an exponential distribution is calculated using the formula:

Variance = θ²

This highlights that the variance is directly dependent on the square of the scale parameter. Since θ represents the average time until an event occurs, the square of this parameter provides insight into the spread of the distribution.

Given this understanding, θ² stands out as the correct answer regarding the variance of an exponential distribution. It accurately represents the relationship between the variance and the scale of the distribution, aligning with the properties of exponential random variables.

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