It has been suggested in statistical literature that scores

It has been suggested in statistical literature that scores in a hockey game may be modeled by two independent Poisson distributions, where each team has a separate scoring parameter lambda. At the World Junior Championships in 2011, Canada met Russia in the finals. Suppose Team Canada has a scoring rate of 7.3 goals per game (lambda_C = 7.3) and Team Russia has a scoring rate of 5.6 goals per game (lambda_R = 5.6). Under the independent Poisson assumptions... What\'s the probability that Russia wins the game 5-3? How many goals would we expect Canada to score in the third period? What\'s the probability that in the third period Canada scores no goals while Russia scores 5? (Regulation hockey games consist of 3 equal length periods)

Solution

The probability mass function for Poisson distribution is

Given that _c =7.3

= 0.1698

f(x) = N*P(x)

= 60 *

Which is the expected number of goals