Statistic Notes 4
Statistic Notes 4 PUBHLTH391B
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This 3 page One Day of Notes was uploaded by Eveline DeJesus on Tuesday January 20, 2015. The One Day of Notes belongs to PUBHLTH391B at University of Cape Town taught by Gregory Matthews in Fall. Since its upload, it has received 103 views. For similar materials see Intro to BioStats in Public Health at University of Cape Town.
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If Eveline isn't already a tutor, they should be. Haven't had any of this stuff explained to me as clearly as this was. I appreciate the help!
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Date Created: 01/20/15
Probability Experiment a procedure that can be repeated amp has a well de ned set of outcomes Sample sbace all the possible outcomes of an experiment 0 roll a dice 16 0 ip a coin heads or tails o ip TWO coins four possible outcomes 0 TWO die 36 possible outcomes Event any subset of sample space 0 quotNuquot still a set but still contains no elements not the same as nothing Deterministic Experiment an experiment with only one possible outcome Random Experiment more than one possible outcome Probability Measure 0 Assign probability between 01 cannot be larger than 1 o Closer to 1 more likely it will occur closer to 0 less likely to occur 0 This represents how certain we are about an event in the sample space 0 The total probability of all outcomes in sample space is 1 o If all events in sample space are equally likely the probability of each event is 1ns ns is the number of elements in the sample space 0 Equation Pevent nN o n number of elements in the event N is the number of elements in the sample space Consider two events A and B from sample space S o Complement of A Ac all events in 5 that are not in A 0 Union ofA and B A U B All events inA OR B o Intersection of A and B A U B upside down U All events in A AND B if two events are mutually exclusive if no events in common events cannot occur at the same time Nul Examples of each in notes Principles of Counting if M objects in one group and N objects in another group different number of possibilities is MN o Factorials nnn1n2n3etc o Combinations given a set of N objects how many ways are there to choose R objects from N out of 12 choose 5 how many different combinations of 5 Formula in notes In R code choose53 out of 5 variables how many different combinations of 3 can we make If ip coin three times what probability of observing exactly two tails 0 First part choose32 3 possible ways for event to occur 0 Second part 2quot3 8 0 Probability of getting exactly 2 tails in three coin ips is 38 What is the probability of being dealt 3 of kind How many total hands are there 52 choose 5 How many hands contain three of kind 0 choose525 easy part all possible 5 hands in total deck 0 dif cult part how many of those hands contain three of a kind choose131choose43 now the other two cards in deck must not match three of kind choose121 choose41 choose41 all component over choose525 nal probability 0 Which game is better to play Game 1 Number of ways to win 83 denominator Number of ways to choose three marbles 103 Probability of winningtotal 466 Game 2 95 105 winnertotals 5 higher probability 0 Rules of Probability points 24 more useful 0 Conditional Probability Titanicsurvival data and calculating probability 0 Law of Total Probabilitv take A and partition into two pieces can nd probability by putting pieces together Venn diagram example when a series of disjoint or mutually exclusive nd probability of each individual part then add all together 0 Independence equation If A and B are independent then the probability of A given B is equal to probability of A nothing changes given B Replacing marbles greater probability to win game independence 0 Midterm example Outlier mean has to be above median ine Bayes Theorem see equation Trying to nd B given A but use A given B opposite conditional Event A have the disease 0 Event B tests positive for the disease If know PA can nd PAc by 1PA On exam Same kind of example on exam just different numbers
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