N t has the Poisson pmf p N t n � t nexp λt n n N Sample path of a Poisson

# N t has the poisson pmf p n t n ? t nexp λt n n n

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N ( t ) has the Poisson pmf p N ( t ) ( n ) = ( λ t ) n exp ( - λ t ) n ! , n N Sample path of a Poisson process Vincent Tan (NUS) Poisson Process Feb 2020 3 / 11
Is the Poisson process a good model? An Application Focus on 232 World cup (soccer) games from 1990 to 2002 Vincent Tan (NUS) Poisson Process Feb 2020 4 / 11
Is the Poisson process a good model? An Application Focus on 232 World cup (soccer) games from 1990 to 2002 In the first game of 1990, Cameroon scored a single goal against Argentina at the 67th minute. Vincent Tan (NUS) Poisson Process Feb 2020 4 / 11
Is the Poisson process a good model? An Application Focus on 232 World cup (soccer) games from 1990 to 2002 In the first game of 1990, Cameroon scored a single goal against Argentina at the 67th minute. In the second game, Romania scored 2 goals against the Soviet Union at the 42nd and 57th minutes. Vincent Tan (NUS) Poisson Process Feb 2020 4 / 11
Is the Poisson process a good model? An Application Focus on 232 World cup (soccer) games from 1990 to 2002 In the first game of 1990, Cameroon scored a single goal against Argentina at the 67th minute. In the second game, Romania scored 2 goals against the Soviet Union at the 42nd and 57th minutes. Times to these goals are 65 = ( 90 - 67 ) + 42 and 15 = 57 - 42 min. Vincent Tan (NUS) Poisson Process Feb 2020 4 / 11
Is the Poisson process a good model? An Application Focus on 232 World cup (soccer) games from 1990 to 2002 In the first game of 1990, Cameroon scored a single goal against Argentina at the 67th minute. In the second game, Romania scored 2 goals against the Soviet Union at the 42nd and 57th minutes.

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• Summer '19
• Standard Deviation, Exponential distribution, Association football, Poisson process, Vincent Y. F. Tan

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