What is the expected value of a Poisson distribution?

What is the expected value of a Poisson distribution?

• A. m
• B. n
• C. λ
• D. σ^2

Answer: (C)

The expected value of a Poisson distribution is denoted by the parameter λ (lambda). In a Poisson distribution, which models the number of events occurring within a fixed interval of time or space, λ represents both the average rate of occurrence of events and the mean of the distribution. The expected value provides a measure of the center of the distribution, indicating the long-term average number of events. For a Poisson distribution with parameter λ, it can be derived from the probability mass function and confirms that every Poisson random variable has its mean equal to λ. Thus, the correct answer, λ, clearly reflects the core property of the Poisson distribution, linking the average number of events directly to the expected value.

The expected value of a Poisson distribution is denoted by the parameter λ (lambda). In a Poisson distribution, which models the number of events occurring within a fixed interval of time or space, λ represents both the average rate of occurrence of events and the mean of the distribution.

The expected value provides a measure of the center of the distribution, indicating the long-term average number of events. For a Poisson distribution with parameter λ, it can be derived from the probability mass function and confirms that every Poisson random variable has its mean equal to λ.

Thus, the correct answer, λ, clearly reflects the core property of the Poisson distribution, linking the average number of events directly to the expected value.