Question

In a poisson distribution, the mean and variance are equal.T/F

Answer 1

Answer: True

Step-by-step explanation:

In a Poisson distribution, the mean and variance are both equal to λ, where λ is the parameter that represents the average number of occurrences in a fixed interval of time or space. The probability mass function of a Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable that represents the number of occurrences, k is a non-negative integer, e is the base of the natural logarithm, and k! is the factorial of k.

The mean of a Poisson distribution is given by:

E(X) = λ

and the variance is given by:

Var(X) = λ

Since the mean and variance are equal, it follows that:

E(X) = Var(X) = λ

Answer 2

The statement is True; in a Poisson distribution, the mean and variance are indeed equal, which is a defining property of the distribution.

Step-by-step explanation:

The statement that in a Poisson distribution, the mean and variance are equal is True. By definition, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

The mean of a Poisson distribution is denoted by λ (lambda) and it also represents the variance. Therefore, in a Poisson distribution, the mean and variance are indeed the same value. This is a distinctive property of the Poisson distribution and helps in distinguishing it from other probability distributions. It is used in various fields such as engineering, insurance, finance, and physics to model random events.