S301 Week 5 Lecture & Textbook Notes
S301 Week 5 Lecture & Textbook Notes STAT-S301
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This 3 page Class Notes was uploaded by Lauren Detweiler on Thursday February 12, 2015. The Class Notes belongs to STAT-S301 at Indiana University taught by Hannah Bolte in Spring2015. Since its upload, it has received 98 views. For similar materials see Business Statistics in Statistics at Indiana University.
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Date Created: 02/12/15
S301 Textbook Week 5 Ch 9 amp 12 pgs 200214 267285 Required concepts not covered in lecture Ch 9 I Notations a X random variable b a sigma standard deviation of a random variable 02 is variance c u mu the mean of a random variable The weighted sum of possible values with the probabilities as weights d EX expected value of X Equal to u A weighted average that uses probabilities to weight the possible outcomes e PXx the probability distribution of a random variable 11 Random Variable RV a The uncertain outcome of a random process b Discrete random variable i X is a discrete random variable when we can list all the outcomes ii Takes on one of a list of possible values typically counts c Continuous random variable i X is a continuous random variable when it can take on any value within an interval ii Shows how probability is spread over an interval rather than assigned to speci c values 111 Calculating Parameters for Discrete Random Variables a Calculating u MZZXj39PXx xl PXx1 xz PXx2x3 PXx3x4PXx4 1 b Calculating 02 02 Zxiu2Pxa x u2Px1x2 2Pxzxz2PxsxaM2Px4 1 IV Graphing Discrete RVs a Example V Expected Value a In this class the expected value is always the mean E X M b Adding subtracting a constant from an RV i Shifts every possible value of the RV changing the expected value by the constant ii EX i c EX Ec EX i c iii A shift has no effect on the variance or standard deviation of a random variable c Multiplying a constant with an RV i Changes the mean and standard deviation by a factor of c E cX 2 CE X SDCX cSDX ii Changes the variance by a factor of c VarcX czVarX d Rules for expected values i If a and b are constants andX is a random variable then EabX abEX SDa b X bSDX Vara b X szarX VI Best Practices e Use random variables to represent uncertain outcomes f Draw the random variable g Recognize that random variables represent models h Keep track of the units of the random variables Ch 12 1 Normal Continuous Random Variables i A random variable whose probability distribution defines a standard bell shaped curve j Continuous RV an RV that can conceptually assume any value in an interval ie on a bellshaped curve 11 Central Limit Theorem CLT k The probability distribution of a sum of independent random variables of comparable variance tends to a normal distribution as the number of summed random variables increases Explains why bellshaped distributions are so common m Assures our assumption of normality when considering a sample mean is well founded even if we cannot be entirely sure of the underlying distribution n Shows that extreme observations outliers have less effect as they are averaged in with more typical observations Ill Identifying PZ S 2 By Shading the Bell Curve 0 The first step toward determining the probability of observing a certain data point or sample mean begins with drawing a bell curve marking your mean and i 3 SDs and SHADING the area of interest p a p Example from lecture slides Example What is P O5 3 Z S 1
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