PPT-Probability and Probability Distributions

4 Introduction slide 1 of 3 A key aspect of solving real business problems is dealing appropriately with uncertainty This involves recognizing explicitly that uncertainty exists and using quantitative methods to model uncertainty. AS91586 Apply probability distributions in solving problems. NZC level 8. Investigate situations that involve elements of chance. calculating and interpreting expected values and standard deviations of discrete random variables. 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 . QSCI 381 – Lecture 12. (Larson and Farber, Sect 4.1). Learning objectives. Become comfortable with variable definitions. Create and use probability distributions. Random Variables-I. A . Continuous distributions. Sample size 24. Guess the mean and standard deviation. Dot plot sample size 49. Draw the population distribution you expect. Sample size 93. Sample size 476. Sample size 948. 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. Applied Statistics and Probability for Engineers. Sixth Edition. Douglas C. Montgomery George C. . Runger. Chapter 5 Title and Outline. 2. 5. Joint Probability Distributions. 5-1 Two or More Random Variables. 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 . 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.. 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 . Continuous Probability Distribution . (pdf) . Definition:. . b. P(a . . X.  . b) = .  . f(x). dx. . . a. For continuous RV X & a. .  b.. 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. 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. .