What to do: In short, make at least three quiz problems (with 2-4 sub-questions) covering the materials taught in this course, and complete your own solutions. More specifically, First, find a practical setting for your questions. Just like many examples that we have done in class/homework/practice problems, choose an application context that you find interesting. Examples are (not limited to): customer arrival at the dining hall, CATA bus travels between stops, purchasing some items at a store, how long it takes to make a Latte at a coffee shop, etc. Next, collect some real-world data in the setting that you have picked. It is up to you to determine how many data points you need to collect based on the questions you attempt to design (see the next bullet point). Based on the data that you have collected, design at least three questions that cover at least three of the following topics: o Discrete or continuous probability distributions o Related to the Poisson process (e.g., arrival rate, inter-arrival time) o Related to Normal distribution, standard normal distribution, standardization o Approximation of distributions o Reliability analysis, failure rate, system reliability o Point and interval estimates for your sampling statistics You need to show the depth of your understanding of probability theories and models: Consider the homework/practice/exam questions as the benchmark. For example, o Questions like "how many people ordered a Latte among 100 customers at Starbucks?" would be considered as not relevant. o It would be more appropriate if you ask some questions like "Based on the observed purchases from customers in a coffee shop, what is the probability that at least 10 customers bought regular coffee among randomly arrived 50 customers?" o A good strategy is to make several sub-questions as we have done in many homework/exam questions, which reflect different aspects of your probability models (e.g., connections between exponential and Poisson distribution, between geometric and negative binomial distribution, and using one distribution to approximate another one) Data collection does not have to be fully completed before you start to design your questions. They could go forward together, as you might need to revise your data collection plan based on the questions that you would like to address. regarding the proposal in the last section of this document. Submissions without the approved proposal will not be graded. o Motivation and background. A short paragraph stating your motivation, and clearly describe your application background (i.e., problem context). o Data collection. In a short paragraph, briefly describe where, how, and what have you collected. o Questions and solutions. Clearly state your questions, and provide a detailed solution for each question with rigorous probability statements. Submit (1) the supporting file of your collected data (text or Excel file), and (2) the final report in PDF format, on Canvas. No hard copy will be accepted. How it is graded: From this project, you can earn at most 5 bonus points to your final grade. Your case study will be evaluated by the following criteria: o (20%) Is the data collection process reasonable? 0=poorly designed 5=carefully designed o (40%) Are the probability questions clearly stated and do they demonstrate certain difficulty level? 0=vague and trivial 5=clear and demonstrating in-depth knowledge 0=Non-standard math notations and unclear logic 5=Standard notation, precise and concise statements (Good benchmarks are solutions to examples in the textbook)