AEM 201 1st Edition Lecture 11PREVIOUS LECTUREI. Relationship of ProbabilityII. Discrete Probability of DistributionCURRENT LECTUREI. Some Important Discrete Probability DistributionsSOME IMPORTANT DISCRETE PROBABILITYDISTRIBUTIONS- Discrete Uniform Probability Function: express the probabilities of outcomes for a discrete random variable x for which all possible outcomes are equally likelyo Given by: F(x)= 1/n if x is in the set. 0 otherwiseo Discrete: limited outcomeso Uniform: all equally likelyo Where n equals the number of possible unique values that the randomvariable x may assume- Know if the end points are included in the range- Add the probability if all variables are discrete and equally likely- Binomial Probability Function: mathematical expressions of the probability of the number of ‘successes’ (x) in n identical trialso Characteristics of a binomial experiment are: Experiment consists of a sequence f n identical trials There are two possible outcomes on each trial The probability of ‘success’ (denoted p) is constant across trials The trials are independent- Trials are independent, so we can multiply their probabilities directly- The binomial probability distribution function is:- F(x)=the probability of x successes in n trials- n=the number of trials- p=probability of success- x=number of successGradeBuddy- 1-p=probability of failure- Sometimes it’s easier to find the complement of the probability you are tryingto find and subtract that from one- Success does not necessarily mean something good it just means the outcomeyou are looking at- Note that binomial probability tables (available in many textbooks) can be used for certain values of p, n, and xo Also note that E(x)==npo V(x)=standard deviation squared=np(1-p)=npq- The probability curve and distribution for the previous problem (a binomially distributed random variable with a probability 0.5 looks roughly symmetrical)- Poisson Probability Function: mathematical expression of the probability for the number of random, independent occurrences (x) of a relatively rare eventover some interval or continuum o Characteristics of a Poisson experiment are: The probability of an occurrence is the same over any two intervals of equal length The occurrence or nonoccurrence in any interval is independent of the occurrence or nonoccurrence in any
View Full Document
Unlocking...