Question

During a recent 46-year period, New York State had a total of 194 tornadoes that measured 1 or greater on the Fujita scale. Let the random variable x equation represent the number of such tornadoes to hit New York State in one year, and assume that it has a Poisson distribution.

What is the variance of the numbers of such New York tornadoes in one year?

Answer 1

The variance of the number of tornadoes in New York State in one year, given that it follows a Poisson distribution, is equal to the mean number of tornadoes per year, which is approximately 4.217.

Step-by-step explanation:

The question is asking for the variance of the number of tornadoes hitting New York State in one year, assuming that it follows a Poisson distribution.

By definition, for a Poisson distribution, the mean (λ) is equal to the variance.

To find the mean number of tornadoes per year, we divide the total number of tornadoes by the number of years: 194 tornadoes / 46 years = 4.217 tornadoes per year (approximately).

Since the mean and variance of a Poisson distribution are the same, the variance is also 4.217.