create Discrete Distribution Poisson question Questions must be of your own crea

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create Discrete Distribution Poisson question
Questions must be of your own creation and should be framed within a content-appropriate "real-life" (or imaginary) context or scenario.
Each question will be evaluated based on the following criteria:
1. Question 1:
5 pts - problem requires the use of the discrete distribution assigned and convinces me you understand the statistical concepts involved 5 pts - problem is framed within a content-appropriate "real-life" (or imaginary) context or scenario and is logical, clear and well-written 5 pts - correct solution is provided with thorough explanations and work create Discrete Distribution Poisson question
Questions must be of your own creation and should be framed within a content-appropriate "real-life" (or imaginary) context or scenario.
Each question will be evaluated based on the following criteria:
1. Question 1:
5 pts - problem requires the use of the discrete distribution assigned and convinces me you understand the statistical concepts involved 5 pts - problem is framed within a content-appropriate "real-life" (or imaginary) context or scenario and is logical, clear and well-written 5 pts - correct solution is provided with thorough explanations and work create Discrete Distribution Poisson question
Questions must be of your own creation and should be framed within a content-appropriate "real-life" (or imaginary) context or scenario.
Each question will be evaluated based on the following criteria:
1. Question 1:
5 pts - problem requires the use of the discrete distribution assigned and convinces me you understand the statistical concepts involved 5 pts - problem is framed within a content-appropriate "real-life" (or imaginary) context or scenario and is logical, clear and well-written 5 pts - correct solution is provided with thorough explanations and work

Explanation / Answer

My example - Whatsap* messages

I receive several whatsap* messages everyday just like anyone else, from all the groups that i'm in and from my friends and relatives, all put together. I always wondered at the pattern of receiving whatsap* messages. If i calculate the average number of messages that i receive looking at the past data or somehow take the readings of number of messages that I receive on an hourly basis, it is averaging around 90 messages every hour which is almost like 1.5 messages every minute.

Message is definitely a discrete variable. It cannot carry a continuous number but a discrete number. And if I assume that number of messages that I receive between any two hours (any two periods of interval) is same and that the number of messages that I receive between any two hours is independent of receiving messages between any other two hours, then the pattern of receiving whatsap* messages is actually following Poisson probability distribution.

The poisson probability function for the above situation of receiving whatsap* messages can be shown as

P(r) = (90r e-90) / r! where r is the number of messages received in one hour.

This can also converted in minutes, and it would be

P(r) = (1.5r e-1.5) / r! where r is the number of messages received in one min.

Many questions like what could be the probability of receiving 100 messages in one hour? What could be probability of receiving 3 messages in one min etc.

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