PPT-Chapter 2. Foundations of Probability

Section 23 Definition of Probability Jiaping Wang Department of Mathematical Science 01162013 Wednesday Outline Introduction Definition of Probability InclusiveExclusive Principle. Section 2.4. Counting Rules Useful in Probability. Jiaping. Wang. Department of Mathematical Science . 01/23/2013, Wednesday. Outline. Fundamental Principle of Counting. . . Permutations. . The Geometric Model. Geometric Probability Model.  . p = probability of success . q = probability of failure = 1-p. X = number of trials until first success.  . Example: . A basketball player has made 80% of his foul shots during the season. What’s the expected number of shots until he makes a shot?. Probability Terminology. Classical Interpretation. : Notion of probability based on equal likelihood of individual possibilities (coin toss has 1/2 chance of Heads, card draw has 4/52 chance of an Ace). Origins in games of chance.. 3.1 . The Concept of Probability. 3.2 . Sample Spaces and Events. 3.3 . Some Elementary Probability Rules. 3.4 . Conditional Probability and Independence. 3.5 . Bayes’ Theorem. 3-. 2. Probability Concepts. Section 5.1. Randomness, Probability, and Simulation. HAPPY HALLOWEEN!!!!!!. Example 1: . When you toss a coin, there are only two possible outcomes, heads or tails. The figure below on the left shows the results of tossing a coin 20 times. For each number of tosses from 1 to 20, we have plotted the proportion of those tosses that gave a head. You can see that the proportion of heads starts at 1 on the first toss, falls to 0.5 when the second toss gives a tail, then rises to 0.67, and then falls to 0.5, and 0.4 as we get two more tails. After that, the proportion of heads continues to fluctuate but never exceeds 0.5 again.. Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 2 Title and Outline. 2. 2. Probability. 2-1 Sample Spaces and Events . 2-1.1 Random Experiments. 2-1.2 Sample Spaces . Section 5-3 – Normal Distributions: Finding Values. A. We have learned how to calculate the probability given an . x. -value or a . z. -score. . In this lesson, we will explore how to find an . More Practical Problems. Jiaping. Wang. Department of Mathematics. 04/24/2013, Wednesday. Problem 1. Suppose we know in a crab farm, 20% of crabs are male. If one day the owner catches . 400 crabs. , what is the chance that more than 25% of the 400 crabs are male?. Continuous Probability Distribution . (pdf) . Definition:. . b. P(a . . X.  . b) = .  . f(x). dx. . . a. For continuous RV X & a. .  b.. A value between zero and one that describe the relative possibility(change or likelihood) an event occurs.. The MEF announces that in 2012 the change Cambodia economic growth rate is equal to 7% is 80%.. . 3.1 - Random Variables. 3.2 - Probability Distributions for Discrete. Random Variables . 3.3 - Expected Values. 3.4 - . The Binomial Probability Distribution. 3.5 - Hypergeometric and Negative. Introduce the Java programming language. Program compilation and execution. Problem solving in general. The software development process. Overview of object-oriented principles. Java Foundations, 3rd Edition, Lewis/DePasquale/Chase. Chapter 5: Investigating DNA. Major Topics. 5.1 DNA Isolation,  Sequencing, and Synthesis. 5.2 Bioinformatics. 5.3 Cloning and Recombinant Expression. 5.4 Microarrays. 5.5 In Situ Hybridization. Foundations of Biochemistry.