PPT-Basic Probability Distributions

How can it be that mathematics being after all a product of human thought independent of experience is so admirably adapted to the objects of reality Albert Einstein Some parts of these slides were prepared based on . Fred Davies. ASTR 278. 2/23/12. Contents. Eddington Ratio. What does it mean?. How do we measure it?. Contents. Eddington Ratio. What does it mean?. How do we measure it?. Two regimes of measurement. 2/29/2012. Review. When playing roulette at the Bellagio casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 13 or to bet $5 that the outcome is any one of these five possibilities: 0 or 00 or 1 or 2 or 3. From Example 8, we know that the expected value of the $5 bet for a single number is -26₵. For the $5 bet that the outcome is 0 or 00 or 1 or 2 or 3, there is a probability of 5/38 of making a net profit of $30 and a 33/38 probability of losing $5.. Understanding the meaning of the terminology we use.. Quick calculations that indicate understanding of the basis of methods.. Many of the possible questions are already sprinkled in the lecture slides.. Objective. : . To solve multistep probability tasks with the concept of geometric distributions. CHS Statistics. A . Geometric probability model. . tells us the probability for a random variable that counts the number of . Binomial distributions. are models for some categorical variables, typically representing the . number of successes. in a series of . n. independent trials. . The observations must meet these requirements: . A Brief Introduction. Random Variables. Random Variable (RV): A numeric outcome that results from an experiment. For each element of an experiment’s sample space, the random variable can take on exactly one value. Maryam . Aliakbarpour. (MIT). Joint work with: Eric . Blais. (U Waterloo) and . Ronitt. . Rubinfeld. (MIT and TAU). 1. The Problem . 2. R. elevant features in distributions.  . Smokes. Does not regularly exercise . 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.. What we learned last class…. We are not good at recognizing/dealing with randomness. Our “random” coin flip results weren’t streaky enough.. If B/G results behave like independent coin flips, we know how many families to EXPECT with 0,1,2,3,4 girls.. II. BINOMIAL DISTRIBUTIONS A. Binomial Experiments 1. A binomial experiment is a probability experiment that satisfies the following conditions: a. The experiment is repeated for a fixed number of independent trials. Copyright © Cengage Learning. All rights reserved. 5 Joint Probability Distributions and Random Samples Copyright © Cengage Learning. All rights reserved. 5.4 The Distribution of the Sample Mean How . can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects . of reality. Albert Einstein. Some parts of these slides were prepared based on . It is also known as the Gaussian distribution and the bell curve. .. The general form of its probability density function is-. Normal Distribution in . Statistics. The normal distribution is the most important probability distribution in statistics because it fits many natural phenomena. . R Programming. By . Dr. Mohamed . Surputheen. probability distributions in R. Many statistical tools and techniques used in data analysis are based on probability. . Probability . measures how likely it is for an event to occur on a scale from 0 (the event never occurs) to 1 (the event always occurs). .