Part 0: Probability Distribution and Expected Value A probability distribution summarizes the outcomes and corresponding likelihood of each outcome. Using a concept similar to a weighted mean, the average or expected value of the probability distribution can be computed. Part 1: Project Data 1) How many total projects are in the data set? 2) How many of them reached their funding goal (i.e., had pledges that reached or exceeded the goal)? What percentage of all the projects reached their funding goal? 3) There are four years of data: 2012, 2013, 2014, and 2015. What percentage of projects in the data set reached their funding goal each year? Year (of End Date) Number of Projects Number of Projects that Reached Goal Percent of Projects that Reached Funding Goal 2012 58.75% 2013 62.50% 2014 2015 4) Is the average of the four percentages in the table above equal to the percentage from question 2) (the percentage of all projects that reached their funding goal)? Why or why not? 5) What percentage of all projects under the Technology category parent reached their funding goal? 6) Did a higher percentage of projects under the Software category or the Apps category reach their funding goal