For poisson distribution, the mean and variance are related by;a.μ>σ2𝜇>𝜎2b.None of allc.μ=σ2𝜇=𝜎2d.μ<σ2

Break Down the Problem

1. We need to examine the relationship between the mean (μ) and variance (σ²) in a Poisson distribution.
2. Identify the correct relationship from the provided options.

Relevant Concepts

1. In a Poisson distribution, the mean (μ) and variance (σ²) are defined as follows:
   • Mean (μ) = λ (the rate parameter)
   • Variance (σ²) = λ

Analysis and Detail

1. For a Poisson distribution:
   • By definition, we have $\mu = \lambda$ and $\sigma^2 = \lambda$.
   • Therefore, it follows that $\mu = \sigma^2$.

Verify and Summarize

1. Since both the mean and variance are equal in a Poisson distribution, the relationship can be succinctly summarized as:
   • $\mu = \sigma^2$.

Final Answer

c. $\mu = \sigma^2$