PPT-Chapter 5: Probability: What are the Chances?

Section 51 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 05 when the second toss gives a tail then rises to 067 and then falls to 05 and 04 as we get two more tails After that the proportion of heads continues to fluctuate but never exceeds 05 again. Corpora and statistical methods. In this lecture. Overview of rules of probability . multiplication rule. subtraction rule. Probability based on prior knowledge. conditional probability. Bayes’ theorem. A-16. If Set X = {13,19,22,26,37} and Set Y = {8,19,37,44,103}, what is the intersection of sets x and y?. Problem . A-17. Simplify:. 15x + 3y – 6x + 3 + 5y =. Problem . A-18. For sets R and S, determine the value R ∩ S.. Independent Events. Events can be "Independent", meaning each event is . not affected. by any other events.. Example: Tossing a coin.. Each toss of a coin is a perfect isolated thing. . What it did in the past will not affect the current toss.. To . define. . what is meant by life chances.. To . explain. how an individual's life chances are influenced by gender, ethnicity, social class and age. .. Life is like a lottery. – discuss this statement.. of winning. The real difference. between winners and . losers in life – . is understanding . your . chances…. Slinky’s casino. 2. Each player has 15 chips.. How will you spend them?. The chips. Probabilistic . Models + Bayes. ’ Theorem. Probabilistic Models. o. ne of the most active areas of ML research. . in last 15 years. foundation of numerous new technologies. e. nables decision-making under . 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. 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%..