Probability Calculus
description
Transcript of Probability Calculus
![Page 1: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/1.jpg)
PROBABILITY CALCULUSFarrokh Alemi Ph.D.
![Page 2: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/2.jpg)
1. Co-occurring2. One of two occurring3. One occurring after
another
Probability Calculus
![Page 3: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/3.jpg)
What is probability?
Probability of A =
![Page 4: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/4.jpg)
OneTwo or more
Joint & Marginal
![Page 5: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/5.jpg)
Two Events Occurring
![Page 6: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/6.jpg)
One or Other Event Occurring
![Page 7: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/7.jpg)
One or Other Event Occurring
![Page 8: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/8.jpg)
HMO Market Penetration
![Page 9: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/9.jpg)
HMO Market Penetration
![Page 10: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/10.jpg)
Mutually Exclusive Outcomes
![Page 11: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/11.jpg)
Mutually Exclusive Outcomes
=0
![Page 12: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/12.jpg)
Addition Rule
![Page 13: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/13.jpg)
Addition RuleP(A, B, …, or Z) = P(A)+P(B)+ … +
P(Z)
![Page 14: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/14.jpg)
Do One: Computers Infected
![Page 15: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/15.jpg)
Events Co-Occurring
![Page 16: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/16.jpg)
Conditional Probabilities
![Page 17: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/17.jpg)
Shrinking Universe of Possibilities
A
![Page 18: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/18.jpg)
Shrinking Universe of Possibilities
A
![Page 19: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/19.jpg)
Shrinking Universe of Possibilities
A
![Page 20: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/20.jpg)
Shrinking Universe of Possibilities
A
![Page 21: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/21.jpg)
Shrinking Universe of Possibilities
A
![Page 22: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/22.jpg)
Shrinking Universe of Possibilities
A
![Page 23: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/23.jpg)
Shrinking Universe of Possibilities
A
![Page 24: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/24.jpg)
Shrinking Universe of Possibilities
A
![Page 25: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/25.jpg)
Shrinking Universe of Possibilities
![Page 26: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/26.jpg)
Shrinking Universe of Possibilities
![Page 27: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/27.jpg)
Shrinking Universe of Possibilities
![Page 28: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/28.jpg)
Hospitalization of Frail Patients
![Page 29: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/29.jpg)
Multiplication Rule
![Page 30: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/30.jpg)
Example of Multiplication Rule
P(Male & Frail) = P(Frail | Male) * P(Male)
![Page 31: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/31.jpg)
Independence
P(B|A) = P(B)
![Page 32: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/32.jpg)
Example
P(Jim|Joe) = P(Jim)
![Page 33: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/33.jpg)
ExampleP(Jim|Joe)
not the same as P(Jim)
![Page 34: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/34.jpg)
Multiplication Rule Simplified
![Page 35: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/35.jpg)
Example
P(Joe & Jim) = P(Joe|Jim) × P(Jim)
P(Joe)
![Page 36: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/36.jpg)
Conditional probability is calculated from reduced sample space
Take Home Lesson
![Page 37: Probability Calculus](https://reader035.fdocuments.in/reader035/viewer/2022062501/568163a8550346895dd4b845/html5/thumbnails/37.jpg)
1. Probability of getting a virus if computer has a spy?2. Probability of getting a spy, if computer has a virus?3. Probability of computers having both?4. Probability of infected computer?
Do one