Question

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

Answer 1

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.