Question

When we list out different distributions (such as the Poisson distribution), we include what are called parameters. Define 'parameters' in your own words using 1-3 sentences.

Answer 1

In statistical distributions like the Poisson distribution, parameters are numerical characteristics that define the distribution. The main parameter for the Poisson distribution is the mean occurrence rate, which determines the probability of a given number of occurrences within a specific interval.

Step-by-step explanation:

Parameters in statistical distributions like the Poisson distribution are numerical characteristics that define the shape and probabilities of the distribution. In the context of the Poisson distribution, the main parameter is the mean occurrence rate (μ), which is the known average rate at which the events occur in a given interval.

This parameter helps determine the probability of a given number of occurrences within that interval. For example, if a book editor knows that there are, on average, five words spelled incorrectly in 100 pages, then the mean (μ) would be 5 for the Poisson distribution modeling this scenario.

The Poisson distribution is also characterized by the Poisson random variable X, which represents the number of events in the interval of interest. The values that X can take on are the non-negative integers (0, 1, 2, 3, ...).

The distribution is defined by its probability mass function (PMF), which calculates the probability of X taking on a particular value.