From the notes of Schroder, Bernd. The Binomial Distribution, Retrieved from; https://www2.latech.edu/~schroder/slides/stat/binom_dist.pdf we have a clear idea what are a binomial distribution and few real life examples.
A distribution can be identified as a binomial distribution if it is consists of fixed number of independent Bernoulli trials having only two outcomes for each trial which can be categorized as success and failure, and the probability of success (or failure) is same from trial to trial.
One example of real-world binomial distribution is the tossing of a coin say 10 times. Here each toss are independent, the outcomes can be categorized into two categories (say head means success), probability of getting head in each toss is fixed and thus this is a perfect example of Binomial distribution.
Now a Poisson distribution is exactly same as the Binomial distribution just one major difference is there, for Poisson distribution the number of trials is not fixed and it can go upto infinity. Rest of the conditions is exactly same and that's how we differentiate between Binomial and Poisson distribution.
Also there are plenty of real world examples for Poisson distribution as provided by Letkowski, Jerzy. Applications of the Poisson probability distribution.Retrieved from https://www.aabri.com/SA12Manuscripts/SA12083.pdf. I am considering the example "The number of arrivals at a car wash in one hour (Anderson et al., 2012, p. 236)."
There are also other examples given in the source, all examples of Poisson distribution as each of the examples are following the conditions to satisfy it as a Poisson distribution.
Sources:
• https://www2.latech.edu/~schroder/slides/stat/binom_dist.pdf
• https://www.statisticshowto.com/what-is-a-binomial-distribution/
• https://www.aabri.com/SA12Manuscripts/SA12083.pdf
This is the questions for my answer above: And just help me with this question;
So, you said that tossing a coin 10 times was an example of a binomial experiment. How would you calculate the probability of having exactly 6 tails out of 10 tosses? Up to and including 6 tails? Please show your calculations and share your formulas!
For Poisson distribution, can you please provide a calculated example as well?