S3 Poisson Calculations

Examples of probability for Poisson distributions[edit]

On a particular river, overflow floods occur once every 100 years on average. Calculate the probability of k = 0, 1, 2, 3, 4, 5, or 6 overflow floods in a 100-year interval, assuming the Poisson model is appropriate.

Because the average event rate is one overflow flood per 100 years, λ = 1

EXERCISE: Use EXCEL to create a table of probabilities for higher values of K and find the value of K for which probabilities fall below 1 in 1000.

Ugarte and colleagues report that the average number of goals in a World Cup soccer match is approximately 2.5 and the Poisson model is appropriate. ^[4]

Because the average event rate is 2.5 goals per match, λ = 2.5.

If there are 200 matches played in the World Cup in a given year, about how many matches would be scoreless by the end of the alloted time? In such matches, overtime is given until one of the two teams scores a single goal, which ends the match.

How many matches would have 5 goals in total?