Normal Random Variable - STAT 200 Sections 1-3 - Class Notes

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1Normal Random VariableStat 200 Sections 1-3Mon Feb 2, 2015LQ5 available after classExam 1 Info is posted(Can list topics for review Session under

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Which as defined is a binomial random variable?For responses from a random sample of10PSU students, the:A. X = number of textbooks bought at the beginning of the semester-discrete, non-binomialB. X = number of students who are on twitter(binomial, how many are on twitter outof 10) 0-10/N)C. X = student’s blood level of Vitamin D (ng/ml)-continuousD.X = number of times a student plays a computer game until he or she first wins-WAITING n?E.X =time elapsedbetween when student sits in the classroom and first checks his orher phone-continuous

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3Conditions: Binomial Distribution1.nfixed trials2.Two possible outcomesfor each trial (binary data)Success:what youwantFailure:what you don’twant3.Outcomes for each trial areindependent(partly linked to randomized trials)4.Probability of success = ( p )and will remain essentiallyconstantfrom trial to trialNote:ideally should replace to meet this condition–but practically do not replace–in these instances it is okay (when you take a small sample relative topopulation size)Check: if n/N < or equal to .05it does not matter that you have not replacedNote:may not always know value of p5.Variable defined as: X = number ofsuccesseswith a fixed n(ideally, the possible values for this random variable are: 0 to n)Note:original data iscategorical

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4Practical Situations:Form a committee-no replacementnNn/N ≤ 0.05p = 0.5remainsconstant?indepen-dent trialsbinomial?1. Four students arerandomly picked from aclass of 10 women and10 men to serve.4204/20 =.2<.05nonono2. four students arerandomly picked from aclass of 100 women and100 men to serve.42004/200 =.02< .05yesyes,randomyes3. four students arerandomly picked from aclass of 1000 womenand 1000 men to serve.420004/2000 =0.002< .05yesyes,randomyesSuccess =WOMANLet X = number of “womenamong the four selections

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Today’s Goals5

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Recallacountablelist (integers)probability distribution functionassumes arangeof valuesprobability density function

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7Example 1: Discrete Probabilities (previous)kP(X = k)00.110.320.430.21.0pdfX= number of courses taughtQuestions:What isthe probability that X is :•exactly 1?P(x=1) =.3•greater than 1?P(x>1) =.6•at least 1?P(x>/=1) = .9

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(General) Normal:endlessSpecific:Standard Normal:How many?values for:μ =0σ =1μ =ANYvalueσ =ANYvalue,except0random variable:Zapproximaterange of values:-3 to 3= 1.0

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