Exam 2 Note Sheet.docx - Stat 324 Exam 2 Notesheet EXAM ONE...

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Stat 324 Exam 2 NotesheetEXAM ONE STUFFDescriptive Statistics-HistogramsPurpose: Helps us share data-Frequency HistogramBar height = # of observations in each bin (absolute frequency)● Sum of bar heights =sample size-Relative Frequency HistogramBar Height (proportion, percentage, relative frequency) =Frequency/Sample SizeExample: Bin 1 height = (3/20) = .15Sum of Bar height = (20/20) = 1Density HistogramBar Height (density) = relative frequency/bin widthBar area =relativefrequencyExample:Bin 1height = .15/100 = .0015Sum ofbar area = 1Larger sd on graph: median~meanNumerical Summary Measures-Location (central tendency, center, average)Median: Rank based central value (½ data smaller, ½ data larger)QuartilesEven: the median, find the medians of the two setsOdd: median as the center value and use that value in both sidesPercentiles vs Quartilestaller than 80% = 80th percentileQ1=25th percentile, Q2=50thPercentile vs Critical Valueskth percentile is k% of data below. (100-k)% aboveMean: Arithmetic averageNotations:Population mean (μ), Sample mean (ȳ), Other cases (E(Y))-Properties of Frequentist ProbabilityP(A) - probability of event A = (#of outcomes in A)/(total # of different outcomes)0<=P(A)<=1P(A) = 1: event A always happensP(A) = 0: event A never happensAddition RuleP(A or B) = P(A) + P(B) if no overlapping (disjoint)Complementary eventsP(not A) = 1- P(A)-Independent Events: The occurrence of the first event does not change the probability of the occurrence of the second eventProduct ruleP(A and B) = P(A) * P(B)-Bernoulli DistributionWe call a RV a Bernoulli RV if it can only realizeto the values 0 or 1, and the probability that it realizes to 1 is called π. A Bernoulli RV X can be denoted as X~Bern(π)If X~Bern(π) then E(X)=πand VAR(X)=π(1-π)-Binomial Random Process (Discrete RV)3. π: The success rate for every trial is the same4. The trial are independentex: flipping a fair coin four times (n = 4, π = .5)Binomial RV and its pmfB ~ Bin(n, π)= total number of successes achieved in n trials of a binomial random process with probability π of success on any trialb ranges from 0 to nExpectation: E(B) = nπVariance: VAR(B) = nπ(1-π)b (pmf)p(b)B=0,1,...,nn!

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