Consider all the activities involved with getting ready for work (or school) every morning, from the...

Consider all the activities involved with getting ready for work (or school) every morning, from the moment you wake up to the moment you walk out the door. What activities might be modeled using discrete random variables? Describe the activity and how the results of the activity are described by the discrete distribution. Try to find at least one example for both the binomial and Poisson probability distributions.

Expert Solution

A practical example of using a binomial distribution is predicting how many games Arsenal will win in a season. We have a Boolean outcome - whether or not Arsenal wins a game.The number of trials n is fixed - we have 38 games per season. Unfortunately, the probability p of Arsenal winning a particular game is not fixed because in each game they always play a different team. However, since they (mostly) play the same teams every season we can fudge things and say their average probability of winning a game (over a given season).

We can then use this average probability to approximate how many of our trials (games) are successful (result in a victory) - which is equivalent to saying Arsenal’s chances of winning any one game is

The Poisson distribution is used whenever we have counting variables, as others have mentioned. But much more should be said! The Poisson arises asymptotically from a binomially distributed variable when n (the number of Bernoulli experiments) increases without bounds, and pp (the success probability of each individual experiment goes to zero, in such a way that stays constant, bounded away from zero and infinity. This tells us that it is used whenever we have a large number of individually very improbable events. Some good examples are: accidents, such as the number of cars crashes in New York in a day since each time two cars passes/meets there is a very low probability of a crash, and the number of such opportunities is indeed astronomical

orchestra answered 2 years ago

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