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# Midterm Notes STA 013

UCD

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## Popular in Elementary Statistics

## Popular in Statistics

This 4 page Study Guide was uploaded by Nataly Florian on Friday October 16, 2015. The Study Guide belongs to STA 013 at University of California - Davis taught by Joshua Patrick in Summer 2015. Since its upload, it has received 72 views. For similar materials see Elementary Statistics in Statistics at University of California - Davis.

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Date Created: 10/16/15

21 Def of Statsscience of gathering describing and analyzing data Raw Data numbers and labels that have been collected but have not yet been processed in any way Variable characteristic that can differ from one individual to the next Obsv Unit a single individual entity in a study Observ sometimes refers to an observational unit mostly refers to the value of a single measurement Sample size the total number of observational unitsn Pop the collection of all of the individuals in the group of interest Sample a subset of the population Statistic a summary measure of sample data Parameter a summary measure of population data 22 Categquanconsist of labels of descript Of traits of the sample Qual consists of counts or measurements Continuousany value in a given range measurement height Discreteany particular value in a given range of cant take on value in between 2425 Distributionhow often the possible responses occur Locationmeasures of centermeanmedium SpreadvariabilityrangeIQR stnrd Dev Rangemaxmin value Q1 Q3 IQR possible outliers Q115IQR Q315IQR Shapevisual displayshistogramsboxplots 27 Lower quartile median of the lower halfQ1 Upper quartilemedian of the higher halfQs Stand Dev Xi Xi39 0 the measure of variation of data from the mean X X Comput 3 14 196 Empirical X Rule Stand 4 4 016 71 34456 44 About 68 xs xs 82 82 for 5 06 036 Random 5 5 610 3 4 4 6 16 256 Circumone About 95 x 25 x25 822 822 39 39 39 in which the Amman M 1 7 outcome is unpredictable Outcomeis determined but our knowledge of it is uncertain Prob between 0amp1inclusive Zx 72 Relative Freq Z scoretransforms the data from a normal shapemeanampmedium to a normal shapeu0 amp 01 0 in which upop mean ostandard dev 73 Sample spacethe collection of all simple events Eventany collec Of one or more simple events in the sample space Ex PA Complement Event they don t share any of the same outcomesimple events Together they cover the entire space Thus PA PAC1 gtPAC1PA Mutually Events 2 events don t contain any of the same outcomes Thus PA or B PA PB Independent Event when one event occurs or has occurred doesn t change the prob That the other occurs Dependent Event when one occur or has occurred changes the prob that the other occurs Conditional Probif events A amp B are depend then the prob of A given B PAB If PA B PA or PBA PB then A and B are independent 74 Complement Rule to nd the prob that an event does not occur PAC 1PA Add Rule PA or B PA PB PA and B Mult Rule PA and B PAB PB or PBA PB Example A fair coin is tossed twice Ahead on 1st toss Bhead 2nd toss A and Bhead both 1st and 2nd toss A or Bhead 1st or 2nd or both A Find PA 12 B Find PB 12 C Mult Rule nd PA and B 14 D AddRule Find PA orB 34 IdAAB IdmAhA 75 Cond Prob Rule PAB W Bayes Rule PAB PBA APBACPAC Example 80ordered coffee 35biscotti ampcoffee Acoffee Bbiscotti A Find PA80 PA and B 35 B Conditional prob that customer would order biscotti given that she orders coffee PBA 4375 C no biscotti but coffee 5625 81 Random Variableassigns a to each outcome of a random circum Can be either discretecountable list of distinct values gt of commercial reported of chapt type of book of error of left handed in sample of 160 or Continousany value in an interval or collection of intervals gtweight widthexam time car speed length of commercial 82 Discrete Random Variables nding prob for exact outcomes Xthe random variable Ka speci ed value of the random var PXK the prob that the random var is equal K Conditions for Discrete RV 1 Z PXK 1 2 0 S P XZK 31 Three tosses of coin HHH HHT HTH HTI39 THH THT TI39H TIT XTais 0 1 1 2 1 2 2 3 Find pdf for Ydiff between of headstails Find the pdf for Zthe sum of the hedstails K O 1 2 3 1 1 3 1 2 3 PX 18 38 38 18 k I k I CDF Noof 0 1 2 3 4 Jobs X Probabilit 014 039 028 014 005 y O O 1 lt l k l Find PX 2 the probability that a randomly selected student held two or fewer jobs during the past year PX S 2 81 B Find the probability P that a randomly selected student held either one or two jobs during the past year P 067 C Find PX gt 0 the probability that a randomly selected student held at least one job during the past year PX gt 0 86 CDF for X K 0 1 2 3 4 PX 014 053 081 095 1 Ski 21 Def of Statsscience of gathering describing and analyzing data Raw Data numbers and labels that have been collected but have not yet been processed in any way Variable characteristic that can differ from one individual to the next Obsv Unit a single individual entity in a study Observ sometimes refers to an observational unit mostly refers to the value of a single measurement Sample size the total number of observational unitsn Pop the collection of all of the individuals in the group of interest Sample a subset of the population Statistic a summary measure of sample data Parameter a summary measure of population data 22 Categquanconsist of labels of descript Of traits of the sample Qual consists of counts or measurements Continuousany value in a given range measurement height Discreteany particular value in a given range of cant take on value in between 2425 Distributionhow often the possible responses occur Locationmeasures of centermeanmedium SpreadvariabilityrangeIQR stnrd Dev Rangemaxmin value Q1 Q3 IQR possible outliers Q115IQR Q315IQR Shapevisual displayshistogramsboxplots 27 Lower quartile median of the lower halfQ1 Upper quartilemedian of the higher halfQs Stand Dev Xi Xi39 0 the measure of variation of data from the mean X X Comput 3 14 196 Empirical X Rule Stand 4 4 016 71 34456 44 About 68 xs xs 82 82 for 5 06 036 Random 5 5 610 3 4 4 6 16 256 Circumone About 95 x 25 x25 822 822 39 39 39 in which the Amman M 1 7 outcome is unpredictable Outcomeis determined but our knowledge of it is uncertain Prob between 0amp1inclusive Zx 72 Relative Freq Z scoretransforms the data from a normal shapemeanampmedium to a normal shapeu0 amp 01 0 in which upop mean ostandard dev 73 Sample spacethe collection of all simple events Eventany collec Of one or more simple events in the sample space Ex PA Complement Event they don t share any of the same outcomesimple events Together they cover the entire space Thus PA PAC1 gtPAC1PA Mutually Events 2 events don t contain any of the same outcomes Thus PA or B PA PB Independent Event when one event occurs or has occurred doesn t change the prob That the other occurs Dependent Event when one occur or has occurred changes the prob that the other occurs Conditional Probif events A amp B are depend then the prob of A given B PAB If PA B PA or PBA PB then A and B are independent 74 Complement Rule to nd the prob that an event does not occur PAC 1PA Add Rule PA or B PA PB PA and B Mult Rule PA and B PAB PB or PBA PB Example A fair coin is tossed twice Ahead on 1st toss Bhead 2nd toss A and Bhead both 1st and 2nd toss A or Bhead 1st or 2nd or both A Find PA 12 B Find PB 12 C Mult Rule nd PA and B 14 D AddRule Find PA orB 34 IdAAB IdmAhA 75 Cond Prob Rule PAB W Bayes Rule PAB PBA APBACPAC Example 80ordered coffee 35biscotti ampcoffee Acoffee Bbiscotti A Find PA80 PA and B 35 B Conditional prob that customer would order biscotti given that she orders coffee PBA 4375 C no biscotti but coffee 5625 81 Random Variableassigns a to each outcome of a random circum Can be either discretecountable list of distinct values gt of commercial reported of chapt type of book of error of left handed in sample of 160 or Continousany value in an interval or collection of intervals gtweight widthexam time car speed length of commercial 82 Discrete Random Variables nding prob for exact outcomes Xthe random variable Ka speci ed value of the random var PXK the prob that the random var is equal K Conditions for Discrete RV 1 Z PXK 1 2 0 S P XZK 31 Three tosses of coin HHH HHT HTH HTI39 THH THT TI39H TIT XTais 0 1 1 2 1 2 2 3 Find pdf for Ydiff between of headstails Find the pdf for Zthe sum of the hedstails K O 1 2 3 1 1 3 1 2 3 PX 18 38 38 18 k I k I CDF Noof 0 1 2 3 4 Jobs X Probabilit 014 039 028 014 005 y O O 1 lt l k l Find PX 2 the probability that a randomly selected student held two or fewer jobs during the past year PX S 2 81 B Find the probability P that a randomly selected student held either one or two jobs during the past year P 067 C Find PX gt 0 the probability that a randomly selected student held at least one job during the past year PX gt 0 86 CDF for X K 0 1 2 3 4 PX 014 053 081 095 1 Ski

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