Answer to Question #168117 in Statistics and Probability for GEORGETTE IZAC

Question

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, of how either the Poisson or the Exponential distribution could be used to model something in real life. 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.

Answer 1

In addition to its use for staffing and scheduling, the Poisson distribution also has applications in biology (especially mutation detection), finance, disaster readiness, and any other situation in which events are time-independent.

Suppose there is a coronavirus desease which average incidence in a certain region is $\approx$ 8.33 cases per hour (200 cases per day). We consider a random variable $X$(number of cases per hour). Then $X\in\text{Poisson }(\lambda),\ \lambda=8.33.$

We will find the probability $P\{X\geq 20\}\text{ (bigger than 480 cases per day)}.$

Using Excel we get:

$P\{X\geq 20\}\approx 0.00016.$

So this is an impossible event.