MATH1280 Statistics 1 Discussion forum UNIT5
Grades 9.80/0-10
Unit 5 deals with two types of discrete random variables, the Binomial and the Poisson, and two types of continuous random variables, the Uniform and the Exponential. Depending on the context, these types of random variables may serve as theoretical models of the uncertainty associated with the outcome of a measurement.
Give an example, USING YOUR OWN WORDS (NOT TEXT COPIED FROM THE INTERNET), of how either the Poisson or the Exponential distribution could be used to model something in real life (only one example is necessary). You can give an example in an area that interests you (a list of ideas is below). Give a very rough description of the sample space.
If you use an idea from another source, please provide a citation in the sentence and a reference entry at the end of your post. Include a citation even if you paraphrase from a website. Please do not copy blocks of text from the Internet--try to use your own words.
When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable, possibly from one of the types that are presented in this unit, can serve as a model. Discuss the importance (or lack thereof) of having a theoretical model for the situation. People can use models to predict business conditions, network traffic levels, sales, number of customers per day, rainfall, temperature, crime rates, or other such things.
-------------------------------------------------------------------------------------------------------------------------------------------------------
"The Poisson distribution is used as an approximation of the total number of occurrences of rare e,"nts," and its space of "variable is the unbounded collection of integers," so "the Poisson random variable is a convenient model when the maximal number of occurrences of the events in a-priori unknown or is very large" (Yakir, 2011, p.71).
When observing the number of customers visiting a gas station, I use this as an illustration of a Poisson distribution. If 10,000 customers visit a gas station per month, I can estimate that 250 customers visit each day. So 250÷30＝8.333 customers each day, and the average number of customers per hour on weekends is (1,2,3,...).
We can determine the likelihood of customers visiting on weekends by using the Poisson distribution, which shows that 250 customers visit the store daily and the rate at which those customers visit the store each hour on weekends.
P(1) 1÷8.3 = 0.12
P(2) 2÷8.3 = 0.24
P(3) 3÷8.3 = 0.36
I utilize the probabilities above to anticipate the rates at which consumers visit the gas station on weekdays by comparing their probability to those of the weekend. I can also identify whether most of its customers visit on weekends or weekdays.
References
댓글