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- 1. Quantitative Methods for Lawyers Probability & Basic Statistics (Part 1) Class #6 @ computational computationallegalstudies.com professor daniel martin katz danielmartinkatz.com lexpredict.com slideshare.net/DanielKatz
- 2. Basic Probability
- 3. Probability is a measure of how likely it is for an event to happen. We name a probability with a number from 0 to 1. If an event is certain to happen, then the probability of the event is 1 and certain not to happen, then the probability of the event is 0. Coin Flip with a Fair Coin P(H) = .5 P(T) = .5 Basic Probability
- 4. If it is uncertain whether or not an event will happen, then its probability is some fraction between 0 and 1 (or a fraction converted to a decimal number). 0 1 Certain not to happen Equally likely to happen or not to happen Certain to happen 0% 50 % Chance 100%
- 5. Basic Probability Die Dice
- 6. Basic Probability Die Assuming the Die is Fair Probability that (1) You will Roll a 5? (2) Probability you will Roll a 5 if 5 has Just Been Rolled
- 7. Basic Probability Die Assuming the Die is Fair ... This is a Random Event
- 8. Basic Probability http://www.math.csusb.edu/faculty/stanton/m262/intro_prob_models/ intro_prob_models.html
- 9. Basic Probability2 3 4 5 6 7 8 9 10 11 12 Please Calculate the Frequency http://ccl.northwestern.edu/netlogo/models/DiceStalagmite
- 10. Basic Probability 2 1 1/36 3 2 2/36 4 3 3/36 5 4 4/36 6 5 5/36 7 6 6/36 8 5 5/36 9 4 4/36 10 3 3/36 11 2 2/36 12 1 1/36
- 11. Basic Probability Two Dice
- 12. When two events are statistically independent, it means that knowing whether one of them occurs makes it neither more probable nor less probable that the other occurs. the occurrence of one event occurs does not affect the outcome of the occurrence of the other event. Similarly, when we assert that two random variables are independent, we intuitively mean that knowing something about the value of one of them does not yield any information about the value of the other. Statistical Independence
- 13. Example: The number appearing on the upward face of a die the ﬁrst time it is thrown and that appearing on the same die the second time, are independent. e.g. the event of getting a "1" when a die is thrown and the event of getting a "1" the second time it is thrown are independent. Statistical Independence
- 14. Basic Probability: Coins What is the Prob of Heads v. Tails? What is the Prob of TT? What is the Prob of HHH,? What is the Prob of HTT?
- 15. This is Binomial
- 16. Basic Probability With A Deck of Cards
- 17. Note: the Probability Changes when Each Card is Drawn Poker / Blackjack
- 18. Basic Probability A Deck of Cards
- 19. Basic Probability A Deck of Cards 1. A red card 2. A spade 3. Not a spade 4. An ace 5. Not an ace 6. The ace of spades 7. A picture card 8. A number card or ‘not a picture card‘ 9. A card that is either a heart or a club 10. A 4 or 5 but not a spade 11. An even numbered card
- 20. 1. A red card 26/52 ½ 2. A spade 13/52 ¼ 3. Not a spade 39/52 ¾ 4. An ace 4/52 1/13 5. Not an ace 48/52 12/13 6. The ace of spades 1/52 7. A picture card 12/52 3/13 8. A number card or ‘not a picture card’ 40/52 10/13 9. A card that is either a heart or a club 26/52 ½ 10. A 4 or 5 but not a spade 6/52 3/26 11. An even numbered card 20/52 5/13
- 21. Life Expectancy Calculator http://www.msrs.state.mn.us/ info/Age_Cal.htmls
- 22. Quick Primer on Set Theory
- 23. Let's say that our universe contains the numbers 1, 2, 3, and 4. Let A be the set containing the numbers 1 and 2; that is, A = {1, 2}. (Warning: The curly braces are the customary notation for sets. Do not use parentheses or square brackets.) Let B be the set containing the numbers 2 and 3; that is, B = {2, 3}. Then we have the following relationships, with pinkish shading marking the solution "regions" in the Venn diagrams:
- 24. Let's say that our universe contains the numbers 1, 2, 3, and 4. Let A be the set c o n t a i n i n g t h e numbers 1 and 2; that is, A = {1, 2}. Let B be the set c o n t a i n i n g t h e numbers 2 and 3; that is, B = {2, 3}.
- 25. Plot the Probability Distribution for Two Dice
- 26. If You Need Additional Assistance
- 27. Probability: mathematical theory that describes uncertainty Statistics: series of techniques for describing and extracting useful information from data Probability Versus Statistics
- 28. The arithmetic mean (or average) is the sum of a series dividing by how many numbers you added together.
- 29. Sum of Series of Numbers Total # of Numbers in the Series _____________________________________________________________________________ Mean =
- 30. Lets Talk About Notation ... x1, x2, x3 x4 .... xn 5, 7, 11, 13 .... x bar the Nth Term Called
- 31. Lets Talk About Notation ... x1, x2, x3 x4 .... xn 5, 7, 11, 13 .... x bar the Nth Term Called
- 32. Calculating Measures of Central Tendency Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100 Series 2: 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100 Series 3: 55, 60, 75, 77, 80, 83, 83, 83, 88, 91, 93 Please Calculate the arithmetic mean
- 33. Measures of Central Tendency The number that occurs most frequently is the mode. When numbers are arranged in numerical order, the middle one is the median.
- 34. Measures of Central Tendency Series 1: 0, 0, 0, 0, 50, 50, 100, 100, 100, 100 Series 2: 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100 Series 3: 55, 60, 75, 77, 80, 83, 83, 83, 88, 91, 93 Please Calculate the Median & Mode
- 35. Bi Modal Distribution
- 36. Bi Modal Distribution With Other Measures of Central Tendency
- 37. Range Range is the difference between the largest and smallest values in a set of values. For example, consider the following numbers: 1, 2, 4, 7, 8, 9, 11. For this set of numbers, the range would be 11 - 1 or 10.
- 38. Range & Interquartile Range The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles The interquartile range is equal to Q3 minus Q1
- 39. Range & Interquartile Range The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles The interquartile range is equal to Q3 minus Q1 Example: 0, 10, 20, 30, 40, 50, 50, 60, 70, 80, 90, 100
- 40. Visualizing Range & IQR The Box and Whisker Plot
- 41. New York City 31.5 33.6 42.4 52.5 62.7 71.6 76.8 75.5 68.2 57.5 47.6 36.6 Houston 50.4 53.9 60.6 68.3 74.5 80.4 82.6 82.3 78.2 69.6 61 53.5 San Francisco 48.7 52.2 53.3 55.6 58.1 61.5 62.7 63.7 64.5 61 54.8 49.4 Average Monthly Temp
- 42. Visualizing Range & IQR The Box and Whisker Plot From Google Images
- 43. Daniel Martin Katz @ computational computationallegalstudies.com lexpredict.com danielmartinkatz.com illinois tech - chicago kent college of law@

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