Problem 2BSC

Tornadoes 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 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 mean number of such New York tornadoes in one year? What is the standard deviation? What is the variance?

Answer :

Step 1 of 1

Given

Tornadoes During a recent 46-year period, New York State had a total of 194 tornadoes that measured 1 or greater on the Fujita scale.

So, n=194 and x = 46

Let the random variable x represent the number of such tornadoes to hit New York State in one year.

Then we assume that it has a Poisson distribution.

Let the mean number of such New York tornadoes in one year.

If μ is the average number of successes occurring in a given time interval or region in the Poisson distribution, then the mean and the variance of the Poisson distribution are both equal to μ.

E(X) = μ

and

V(X) = σ2 = μ

Then the mean of the formula is

E(X) = μ=

E(X) = μ = 4.217

Therefore the mean μ =4.217

Then the standard deviation is given by

σ =

σ =

σ = 2.053

σ 2.1

Hence the standard deviation σ = 2.1

The variance of the formula is given by

V(X) = σ2 = μ

V(X) = σ2 = 4.217

Therefore the variance is V(X) = 4.217