PPT-Probability and Probability Distribution

Probability and Probability Distribution Dr Manoj Kumar Bhambu GCCBA42 Chandigarh M 919888237733 mkbhambuhotmailcom Probability and Probability Distribution Definitions Probability Rules Application of Probability. 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. 5.1.1 Random Variables and Their Distributions. A random variable is a quantity that (prior to observation) can be thought of as dependent on chance phenomena. . . Toss a coin 10 times. X=# of heads. The Poisson random variable was first introduced by the French mathematician Simeon-Denis Poisson (1781-1840). He discovered it as a limit to the binomial distribution as the number of trials . n. approaches infinity.. Distributions. 6.1 Continuous Uniform Distribution. One of the simplest continuous distributions in all of statistics is the . continuous. uniform distribution. . This distribution is characterized by a density function. Normal distribution. Lognormal distribution. Mean, median and mode. Tails. Extreme value distributions. Normal (Gaussian) distribution. P. robability density function (PDF). What does figure tell about the cumulative distribution function . Unit 4. Introduction. Many decisions in business, insurance, and other real-life situations are made by assigning probabilities to all possible outcomes pertaining to the situation and then evaluating the results. For example, a saleswomen can compute the probability that she will make 0,1,2 or 3 or more sales in a single day. An insurance company might be able to assign probabilities to the number of vehicles a family owns. Once these probabilities are assigned, statistics such as mean, variance and standard deviations can be computed for these events. With these statistics, various decisions can be made.. Random Variables. Definition:. A rule that assigns one (and only one) numerical value to each simple event of an experiment; or. A function that assigns numerical values to the possible outcomes of an experiment.. 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. 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.. 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 . Random variable: A variable whose value is determined by the outcome of a random experiment is called a random variable. Random variable is usually denoted by X. A random variable may be discrete or In this class we will review . how statistics are used to . summarize data, special probability distributions, . their . use in simple applications using Frequentist and Bayesian . methods, and Monte Carlo techniques. Uniform distribution. In statistics, uniform distribution is a term used to describe a form of probability distribution where every possible outcome has an equal likelihood of happening. The probability is constant since each variable has equal chances of being the outcome.. 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. .