Discrete Probability Variables

Required Resources

Read/review the following resources for this activity:

  • Textbook: Chapter 4 (All Sections)
  • Lesson
  • Minimum of 1 scholarly source

EBOOK: OpenStax, Introductory Statistics. OpenStax CNX. Aug 23, 2019


Initial Post Instructions

Topic: Poisson Probability Distribution

The Poisson Distribution is a discrete probability distribution where the number of occurrences in one interval (time or area) is independent of the number of occurrences in other intervals.

April Showers bring May Flowers!! Research the “Average Amount of Days of Precipitation in April” for a city of your choice.

In your initial post,


  1. Introduce the City and State. Let us know a fun fact!
  2. Tell us the average number of days of precipitation in that city for the month of April.
  3. Cite your Source


  1. What is the probability of having exactly 10 days of precipitation in the month of April?
  2. What is the probability of having less than three days of precipitation in the month of April?
  3. What is the probability of having more than 15 days of precipitation in the month of April?


Write a sentence for each of the probabilities explaining what those probabilities mean in context of days of precipitation in your chosen city.

Would any of the situations be considered unusual? Why or Why Not?


Initial Post Content: Addresses all aspects of the initial discussion question(s), applying experiences, knowledge, and understanding regarding all weekly concepts.

Evidence & Sources: Integrates evidence to support discussion from assigned readings** OR online lessons, AND at least one outside scholarly source.*** Sources are credited.*

Professional Communication: Presents information using clear and concise language in an organized manner (minimal errors in English grammar, spelling, syntax, and punctuation).


Credited means stating where the information came from (specific article, text, or lesson). Examples: our text discusses…., The information from our lesson states…, Smith (2010) claimed that…, Mary Manners (personal communication, November 2017)…

**Assigned readings are those listed on the syllabus or assignments page as required reading. This may include text readings, required articles, or required websites.

***Scholarly source – per APA Guidelines, only scholarly sources should be used in assignments. These include peer-reviewed publications, government reports, or sources written by a professional or scholar in the field. Wikipedia, Wikis, .com websites or blogs should not be used as anyone can add information to these sites. For the discussions, reputable internet sources such as websites by government agencies (.gov) and respected organizations (.org) can be counted as scholarly sources. Outside sources do not include assigned required readings.


I chose my neighboring town of Crystal Lake, IL Some history: The present day city of Crystal Lake was originally known as Crystal Ville. It was first settled in February 1836. Beman and Polly Crandall from New York were the first settlers of the area. It was renamed Crystal Lake around 1840. The area which is now downtown Crystal Lake was originally known as the Village of Dearborn.

I found that it rained on 5 days in April 2020. 

https://weatherspark.com/m/13433/4/Average-Weather-in-April-in-Crystal-Lake-Illinois-United-States (Links to an external site.)

Now I need to calculate some probabilities using Poisson.

In probability theory (Links to an external site.) and statistics (Links to an external site.), the Poisson distribution (French pronunciation: ​[pwasɔ̃] (Links to an external site.); in English often rendered /ˈpwɑːsɒn/ (Links to an external site.)), named after French (Links to an external site.) mathematician Siméon Denis Poisson (Links to an external site.), is a discrete probability distribution (Links to an external site.) that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently (Links to an external site.) of the time since the last event.

The POISSON.DIST function syntax has the following arguments:

  • X The number of events.
  • Mean The expected numeric value.
  • Cumulative  A logical value that determines the form of the probability distribution returned. If cumulative is TRUE, POISSON.DIST returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive; if FALSE, it returns the Poisson probability mass function that the number of events occurring will be exactly x.

Example – What is the probability of having exactly 10 days of rain in April?


X = 10

Mean = 4

Cumulative = False

Probability of the event to occur three times: P(10;4) = 410e−4 /10! = 0.005292

Using Excel:  =POISSON.DIST(10,4,0) and the value returned is: 0.005292

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