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A) Write-up as a PDF.

B) Submit R code as an R script file

**DIRECTIONS**: **Choose any 3** of the following random variable probability distributions to investigate:

- Binomial
- Poisson
- Negative Binomial
- Hypergeometric

Complete the following for your PDF write up document. ** Copy and paste THE NUMBERED PROMPTS into your write up document **so that it is clear which prompt you are responding to.

1) Perform an internet search and find a real life application where calculating probabilities using each of your 3 distribution choices is useful for problem solving. include the hyperlink and title of the source location for each of the 3 choices. Label so it is clear which source goes with which probability distribution.

2) In 4-6 sentences, describe the application (one description for each of your choices… so there should be 3 separate application descriptions presented in your writeup ) and how the probability results are being used to inform decision makers. CLEARLY label for which probability distribution that you are providing a sample application response for.

3) In 1 – 2 sentences, be sure to also state why it is reasonable to use the probability approach for the application. That is, share how the application satisfies the conditions of use for the probability distribution.

4) develop a question stem of a sample real-life problem , applicable for your applications presented in 2 above, that can be solved using your probability distribution selection. That is, there should be 3 clearly labeled sample problems. Include the numerical values for each variable needed to calculate the probabilities.

5**) Use R to generate the probabilities** that correctly answer your question stems. Copy and paste the R code snippets into your write up document such that the associated code snippet is DIRECTLY pasted beneath the problem stem to which is applies. That is, there should be snippets of R code beneath each of your 3 problem stems

5) Use R to Generate a histogram of probabilities that could be useful for supplemental interpretation for each of your 3 problems presented. Include a copy of the histograms in your writeup document. Ensure all histograms have chart titles and axes titles. Number your histograms (Using ‘Figure 1’ etc… and provide a brief description.)

6) Interpret your numerical probability result generated by R. Does the magnitude of the probability make sense given the parameters you used? How might a decision maker interpret and use the probability result relative to the issue presented in your problem stem.?

7) Save all R code , to one R script file, and turn it in along with your PDF writeup. Your R code should contain comments so it is clear what is occurring within the code. And variables used should be defined using comments