The variance formula for a geometric distribution is dependent on which parameters?

The variance formula for a geometric distribution is dependent on which parameters?

• A. n and p
• B. q and p
• C. q and λ
• D. p and λ

Answer: (B)

For a geometric distribution, the variance is determined by the probability of success, denoted as \( p \), and the probability of failure, \( q \), where \( q = 1 - p \). The variance formula for a geometric distribution is given by \( \text{Var}(X) = \frac{q}{p^2} \). In this context, \( p \) represents the probability of a success on each trial, while \( q \) represents the probability of a failure. Since the variance relies on both of these probabilities, identifying both \( q \) and \( p \) as the key parameters accurately captures the relationship necessary to calculate the variance. The other options are not applicable because they include a parameter not relevant to the geometric distribution's variance. For example, \( n \) (which refers to the number of trials) is not used in the formulation for the variance of a geometric distribution, as it is memoryless and defined by the number of trials until the first success. The parameters \( λ \) typically relate to the Poisson or exponential distributions, which are not applicable in this case. Thus, \( q \) and \( p \) stand out as the relevant parameters for the variance of a

For a geometric distribution, the variance is determined by the probability of success, denoted as ( p ), and the probability of failure, ( q ), where ( q = 1 - p ). The variance formula for a geometric distribution is given by ( \text{Var}(X) = \frac{q}{p^2} ).

In this context, ( p ) represents the probability of a success on each trial, while ( q ) represents the probability of a failure. Since the variance relies on both of these probabilities, identifying both ( q ) and ( p ) as the key parameters accurately captures the relationship necessary to calculate the variance.

The other options are not applicable because they include a parameter not relevant to the geometric distribution's variance. For example, ( n ) (which refers to the number of trials) is not used in the formulation for the variance of a geometric distribution, as it is memoryless and defined by the number of trials until the first success. The parameters ( λ ) typically relate to the Poisson or exponential distributions, which are not applicable in this case. Thus, ( q ) and ( p ) stand out as the relevant parameters for the variance of a