Explore the challenges and implications of rare and extreme space weather events in this comprehensive lecture by Dan Fry from NASA's Space Radiation Analysis Group. Delve into topics such as solar dips, event data analysis, and statistical approaches to understanding these phenomena. Learn about electronic stopping power, random events, and integrating spectra. Gain insights into the maximum entropy principle and time interval considerations in space weather research. Discover how scientists deal with the complexities of rare space weather occurrences and their potential impacts on space exploration and technology.