Lecture 8—Probability and Statistics (Ch. 3) Friday January 25 th Quiz on Chapter 2 Classical and statistical probability The axioms of probability theory Independent events Counting events Reading: All of chapter 3 (pages ) Homework 2 due TODAY ***Homework 3 due Fri. Feb. 1st**** Assigned problems, Ch. 3: 8, 10, 16, 18, 20 Homework assignments available on web page Exam 1: two weeks from today, Fri. Feb. 8th (in class)

ClassicalThermodynamics

Classical and statistical probability Classical probability: Consider all possible outcomes (simple events) of a process (e.g. a game). Assign an equal probability to each outcome. Let W = number of possible outcomes (ways) Assign probability p i to the i th outcome

Classical and statistical probability Classical probability: Consider all possible outcomes (simple events) of a process (e.g. a game). Assign an equal probability to each outcome. Examples: Coin toss: W = 2 p i = 1/2

Classical and statistical probability Classical probability: Consider all possible outcomes (simple events) of a process (e.g. a game). Assign an equal probability to each outcome. Examples: Rolling a dice: W = 6 p i = 1/6

Classical and statistical probability Classical probability: Consider all possible outcomes (simple events) of a process (e.g. a game). Assign an equal probability to each outcome. Examples: Drawing a card: W = 52 p i = 1/52

Classical and statistical probability Classical probability: Consider all possible outcomes (simple events) of a process (e.g. a game). Assign an equal probability to each outcome. Examples: FL lottery jackpot: W = 20Mp i = 1/20M

Classical and statistical probability Statistical probability: Probability determined by measurement (experiment). Measure frequency of occurrence. Not all outcomes necessarily have equal probability. Make N trialsMake N trials Suppose i th outcome occurs n i timesSuppose i th outcome occurs n i times

Classical and statistical probability Statistical probability: Probability determined by measurement (experiment). Measure frequency of occurrence. Not all outcomes necessarily have equal probability. Example:

Classical and statistical probability Statistical probability: Probability determined by measurement (experiment). Measure frequency of occurrence. Not all outcomes necessarily have equal probability. More examples:

Classical and statistical probability Statistical probability: Probability determined by measurement (experiment). Measure frequency of occurrence. Not all outcomes necessarily have equal probability. More examples:

Statistical fluctuations

The axioms of probability theory 1. p i ≥ 0, i.e. p i is positive or zero 2. p i ≤ 1, i.e. p i is less than or equal to 1 3.For mutually exclusive events, the probabilities for compound events, i and j, add Compound events, (i + j): this means either event i occurs, or event j occurs, or both.Compound events, (i + j): this means either event i occurs, or event j occurs, or both. Mutually exclusive: events i and j are said to be mutually exclusive if it is impossible for both outcomes (events) to occur in a single trial.Mutually exclusive: events i and j are said to be mutually exclusive if it is impossible for both outcomes (events) to occur in a single trial.

The axioms of probability theory 1. p i ≥ 0, i.e. p i is positive or zero 2. p i ≤ 1, i.e. p i is less than or equal to 1 3.For mutually exclusive events, the probabilities for compound events, i and j, add In general, for r mutually exclusive events, the probability that one of the r events occurs is given by:In general, for r mutually exclusive events, the probability that one of the r events occurs is given by:

Independent events Example: What is the probability of rolling two sixes? Classical probabilities: Two sixes: Truly independent events always satisfy this property. In general, probability of occurrence of r independent events is: