1. Probability and Statistics
AME20213 – Measurements and Data Analysis
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2. ALEA IACTA EST “The die is cast!”
Julius Caesar, 49 B.C.
“The die is cast!”
Success often hinges on calculated risks.
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3. Measuring Probability – Poisson Statistics
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4. Measuring Probability – Poisson Statistics
Statistical Repeatability Uncertainty
Total uncertainty includes repeatability and instrument uncertainty
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5. Probability – “Combinatorics”
Probability based on combinations of electors is much harder to predict.
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6. Measuring Probability
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7. Actuarial Science and Public Policy
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8. 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.
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9. Probability – Venn Diagrams
Intersection “AND”
Union “OR”
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10. Probability Trees Genetics Fault Tree Analysis Evolutionary Biology
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11. 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.
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12. Courses at Notre Dame ACMS30530 – Intro to Probability
MATH40210 – Basic Combinatorics
AME50561 – Reliability in Engineering
ACMS20340 – Statistics for Life Sciences
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13. Network Reliability Networks show up everywhere:
Communications (i.e. the internet)
Electrical grids
Social networks
Economics
National Security
6. The Seven Bridges of Königsberg
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14. Socioeconomic Networks
'When we understand that slide, we'll have won the war.' -General Stanley McChrystal
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15. PHYS70152 - Intro to Network Science
Notre Dame has a center for Network Science
Course on network science:
PHYS Intro to Network Science
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16. Monte Carlo Calculations
Counted N = 20,857 bullet holes
Measured
π = 3.132
arXiv: v2
Consider taking random shots at this board.
Probability of landing in the circle:
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17. 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?
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18. Games!
“Plinko” Game
Random Walk
“Drinko” Game
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19. 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.
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20. Gaussian Distribution
Gaussian PDF
Central Limit Theorem – For large N, most distributions become Gaussian
Carl Friedrich Gauss ( )
Gaussian CDF
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21. Student’s t distribution
Need to use this if N < 50
Shorter and wider than Gaussian PDF
PDF
CDF
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22. Log-normal Distribution
Used when distribution has a boundary near the mean.
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25. “Bimodal” distribution
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26. Statistical Mechanics
“Maximum entropy” distribution
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27. Electron Orbitals
Electron orbitals are also probability density functions
(probability per unit volume)
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28. 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
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