Answer: Mean equals the variance

## Explanation For a Poisson distribution with mean λ: 1. **Mean = λ** 2. **Variance = λ** 3. **Standard deviation = √λ** 4. **Median** is approximately λ but not exactly equal to λ (it's approximately λ - 1/3 for large λ) Therefore: - **Mean equals the variance** (both are λ) - This is correct - Mean does NOT equal the standard deviation (mean = λ, standard deviation = √λ) - Median does NOT equal the variance - Median, mean, and variance are NOT all equal This is a key property of the Poisson distribution: **the mean and variance are equal**. This property distinguishes the Poisson distribution from other distributions like the normal distribution (where mean and variance are independent parameters) or the binomial distribution (where variance = np(1-p) ≠ mean = np).

Author: Nikitesh Somanthe