Parameter of Poisson Distribution
The parameter of a Poisson distribution is denoted by λ, which represents the average rate at which events occur. When p(x=4) = p(x=5) in a Poisson distribution, it means that the probability of observing 4 events is equal to the probability of observing 5 events. This implies that the distribution is symmetric around its mean, which is equal to λ.

Explanation
- In a Poisson distribution, the mean (λ) is equal to the variance.
- When p(x=4) = p(x=5), it indicates that the distribution is balanced around its mean.
- Since the mean and variance are equal in a Poisson distribution, the parameter λ remains the same for both probabilities.
- This balance around the mean is a characteristic feature of the Poisson distribution.
- The parameter λ determines the shape and characteristics of the Poisson distribution, such as the average rate of event occurrences.
Therefore, when p(x=4) = p(x=5) in a Poisson distribution, the parameter of the distribution remains constant and equal to the mean (λ).