If 'm' is the mean of a Poisson distribution, then its variance is given by :
Answer: m
Step-by-step solution
Step 1: Recall Poisson Distribution Properties
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.
Step 2: Identify Mean and Variance Relationship
A fundamental property of the Poisson distribution is that its mean and variance are equal. The parameter (lambda) represents both the mean and the variance of the distribution.
Step 3: Substitute Given Mean
The problem states that 'm' is the mean of the Poisson distribution. Since the variance of a Poisson distribution is equal to its mean, the variance will also be 'm'.