Vocabulary Lists and Suggested problems for chapters 4 through 6 Chapter 4 Probability uses population info to make predictions about samples population to sample Essentially the opposite of statistics sample to population MEASURE of how likely an event is Empirical not obvious of the result P A n A n P empirical probability P probability A specific outcomes n A number of times the event A has occurred n total number of times experiment was performed Need lots of evidence Theoretical P A times event A occurs in sample space of outcomes in sample space P A n A n S Subjective personal judgment When outcomes are NOT equally likely and empirical probability can be used but not be available Meteorologists Experiment process that yields 1 result or observation Outcome all possible results Event one outcome of interest Sample space S list of all possible outcomes for an experiment Number of outcomes in S n S S 1 2 3 4 5 6 n S 6 Tree diagram Venn diagram Law of large numbers with repetition empirical results will approach the theoretical probability As n infinity P A P A Odds Complement the probability an event A does NOT occur 1 P A Addition rule when NOT mutually exclusive P A or B P A P B P A and B Multiplication rule Mutually exclusive only one event can occur Addition rule P A or B P A P B Independent Multiplication rule P A and B P A P B One does NOT influence the other if P A and B and NOT independent P A and B P A P B A Compound event Conditional Probabilities P B A the probability that B will ALSO occur given that A has occurred P B A P A and B P A If event A is independent of B then P B P B A Ed 10 4 10 4 14 4 26 4 43 4 61 4 64 4 69 4 72 4 103 4 109 4 127 Ed 9 Problems 4 38 4 48 4 57 4 58 4 75 4 78 4 96 Chapter 5 Random variables variable x whose value depends on the outcome of a chance operation Possible outcomes all possible outcomes of an event Outcome based on chance 1 outcome per run Every outcome independent Numerical Random Variables Discrete random variables quantitative integers Continuous random variables quantitative decimal fractions Probability distribution represent theoretical populations Probability function when each outcome is equally likely P x 1 10 for x 1 2 3 4 5 6 7 8 9 10 Probability histogram Mean and variance for discrete random variables m xP x mean sum of each outcome its probability variance SD2 x m 2 P x To make probability histogram find all probabilities for possible outcomes 1 2 3 4 5 6 Mean and variance for binomial variables equations will be given for both only 2 possible outcomes All binomial are discrete but not all discrete are binomial Binomial probability function Binomial coefficient n x n x P success x P failure n x Can often turn any variable into binomial perspective Ex Dice discrete 6 side outcomes 1 2 3 4 5 6 Binomial even or odd Parasites discrete parasites Binomial infected or not Can also flip non discrete variables Tshirt size ordinal s m l Binomial small or not small Height continuous height in inches Discrete less then 70inches or greater than 70in MOST IMPORTANT DISCRETE DISTRIBUTIONS success vs failure Population parameters binomial distributions m np mean outcomes P success sd2 npq variance outcomes P success P failure 5 is rare probability Could suggest violation of assumptions As p approaches q distribution symmetrical p q skew left graph p q skew right graph as n increases graph becomes less skewed Ed10 5 37 5 71 5 105 Ed 9 5 35 5 73 5 99 Chapter 6 Normal probability Standard normal distribution Standard normal curve Standard score Z equation z notation Normal approximation of a binomial probability GENERAL RULE FOR NORMAL DISTRIBUTION IN BINOMIAL PROBABILTY Normal distribution is reasonable when n p 5 and n 1 p 5 Ed 10 Ed 9 6 17 6 41 6 60 6 80 6 93 6 17 6 54 6 66 6 79