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Midterm

# Statistics Midterm 2 Notes

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UOIT

Business

BUSI 1450U

William Goodman

Winter

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Statistics Midterm 2 InformationChapter 72 Binomial DistributionBinomial distributionspecial case of discrete probability distributionThe word binomial is derived from bi for two and nominal for numbers suggesting a reference to trials such as coin fillips that have only two possible values or numbers that could resultA success denotes the occurrence of an outcome in which we are interested such as tossing a head and a failure denotes obtaining the opposite outcomeA binomial distribution can also be called a trial sometimes called a Bernoulli trial since a trail is a 2 possible outcome random experiment of the sort described aboveEach unique sequence of outcomes for all of the trials combined may define one possible outcome for the overall experimentBinomial experimentan experiment such as the two coin flips that consists of a sequence of identical and independent Bernoulli trialsBinomial random variablea variable that counts the number of successes regardless of exact sequence among the trial results in the binomial experiment These conditions must be met 1 The experiment consists of n identical trials 2 There are only two mutually exclusive results possible for each trial 3 All of the trials are independent 4 The probabilities of success are constant for each trial Calculating the probabilities for a binomial random variable Pa The number of ways A can occur the number of different outcomes possible in the sample space Nfixed number of trials xspecific number of success pprobability of success in one trial 1pprobability of failure in one trial Pxprobability of getting exactly X successes among N trialsExample Number of Tails in 2 Tosses of Coinn2 p05 X PX 01425s 12450 Binomial Probability Distribution FunctionnnXX1PXpp XnX Minitab procedureprobability ofsuccesses givenand PXXnp1 Calc 2 Probability distributionsnumber of successes in sample 01XXn3 Binomial 4 Input the value for X into Input Constant 5 Click Probabilitythe probability of each successpsample sizenFinding Cumulative Binomial ProbabilitiesCalculates the probabilities that X will fall below or above etc a certain value o Find PX for all Xs that meet the specified condition o Add all the probabilities found in step 1 Example Probability of 1 or more Tails in 2 Tosses of Coinn2 p05 X PX 01425 12450 21425In minitab 1 Calc 2 Probability distribution 3 Binomial 4 Input the value for X into Input constant 5 Click Cumulative probabilityResult gives the probability of getting a count less than or equal to the X you type in Chapter 7 MaterialsChapter 8 Material n Miu u P Sigma o X X Has gaps in between underneath the curve Has no gaps

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