Probability and Statistics AME20213 – Measurements and Data Analysis AME20213

ALEA IACTA EST “The die is cast!” Julius Caesar, 49 B.C. “The die is cast!” Success often hinges on calculated risks. AME20213

Measuring Probability – Poisson Statistics http://polling.reuters.com/ AME20213

Measuring Probability – Poisson Statistics Statistical Repeatability Uncertainty Total uncertainty includes repeatability and instrument uncertainty http://polling.reuters.com/ AME20213

Probability – “Combinatorics” Probability based on combinations of electors is much harder to predict. http://www.businessinsider.com/final-electoral-college-map-trump-clinton-2016-11 AME20213

Measuring Probability AME20213

Actuarial Science and Public Policy https://www.ssa.gov/oact/STATS/table4c6.html AME20213

Product Safety People’s lives are in your hands! United Airlines Flight 811 Aloha Airlines Flight 243 Insufficient locking mechanism on cargo bay door of Boeing 747. Rupture in fuselage roof of Boeing 737. AME20213

Probability – Venn Diagrams Intersection “AND” Union “OR” AME20213

Probability Trees Genetics Fault Tree Analysis Evolutionary Biology AME20213

Genetics and Epidemiology Genetic Sequencing: Future Medicine Human genetic sequence consists of over 3 billion base pairs: Big data! Epidemiology – Scientists can monitor the mutations and evolution of diseases in real time. http://dx.doi.org/10.1371/journal.ppat.1000212 AME20213

Courses at Notre Dame ACMS30530 – Intro to Probability MATH40210 – Basic Combinatorics AME50561 – Reliability in Engineering ACMS20340 – Statistics for Life Sciences AME20213

Network Reliability Networks show up everywhere: Communications (i.e. the internet) Electrical grids Social networks Economics National Security 6. The Seven Bridges of Königsberg AME20213

Socioeconomic Networks 'When we understand that slide, we'll have won the war.' -General Stanley McChrystal AME20213

PHYS70152 - Intro to Network Science Notre Dame has a center for Network Science Course on network science: PHYS70152 - Intro to Network Science AME20213

Monte Carlo Calculations Counted N = 20,857 bullet holes Measured π = 3.132 arXiv:1404.1499v2 Consider taking random shots at this board. Probability of landing in the circle: AME20213

Often used to numerically evaluate complex integrals. Monte Carlo Calculations Often used to numerically evaluate complex integrals. i.e. What’s the volume enclosed in these surfaces? AME20213

Games! “Plinko” Game Random Walk “Drinko” Game AME20213

Probability Density Functions Calculate mean and standard deviation. Use CDF or z-table to compute probability. We are essentially “curve fitting” the discrete histogram with a continuous PDF. AME20213

Gaussian Distribution Gaussian PDF Central Limit Theorem – For large N, most distributions become Gaussian Carl Friedrich Gauss (1777-1855) Gaussian CDF AME20213

Student’s t distribution Need to use this if N < 50 Shorter and wider than Gaussian PDF PDF CDF https://en.wikipedia.org/wiki/Student%27s_t-distribution AME20213

Log-normal Distribution Used when distribution has a boundary near the mean. https://en.wikipedia.org/wiki/Log-normal_distribution AME20213

“Bimodal” distribution AME20213

Statistical Mechanics “Maximum entropy” distribution AME20213

Electron Orbitals Electron orbitals are also probability density functions (probability per unit volume) AME20213

Other Courses in Probability AME50561 – Reliability in Engineering (Ovaert) ACMS10145 – Stats for Business I ACMS20340 – Statistics for Life Sciences ACMS30530 – Intro to Probability ACMS30540 – Mathematical Statistics ACMS30600 – Stat Methods & Data Analysis ACMS37020 – Projects in Actuarial Science ACMS40875 – Stat Methods in Data Mining MATH40210 – Basic Combinatorics AME20213