Week6-2up_001 - Wednesday 10/2/02 : Pages 185 – 189,...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Wednesday 10/2/02 : Pages 185 – 189, 210–211 REGULARLY SCHEDULED DISCUSSION SECTION. Tuesday 10/1/02 : EXAM 1–during your bring it to class with you. etc. Suggestion - print out Sample Exam 1 and about homework, course material, sample exam, Monday 9/30/02 : OPTIONAL REVIEW, ask questions us just don’t have film. Thought: We all have photographic memories–some of STA 2023 c D.Wackerly - Review for Exam I 1 inference. 5. Measure of the goodness or reliability of the sample. 4. Inference about population based on info in 3. Sample of population units. 2. Specification of Variables to be investigated 1. Clear specification population of interest Five Elements of a Statistical Problem (p. 8) Sample (p. 5) Variable (p. 4) Population (p. 4) (estimates, decisions) Statistics (p. 2, 3) Descriptive (Communicate) and Inferential Chapter 1 : STA 2023 c D.Wackerly - Review for Exam I ¡ ¡ ¡ ¡ ¡ 2 , “mu” (p. 42) (p. 41) (F.S.) – The mode (p. 44) – Skewness and Symmetry (p. 45) – The median (p. 42-43) – Population Mean : – Sample Mean : – Where is the “middle”? Measure of Central Tendency (p. 40) 68-71, 78-79, ) Box-plots, outliers, scatter diagrams (p. 28–30, ¡ (p. 53) (p. 53) (p. 52) MORE variability. – Variance or standard deviation LARGE Std. Dev. : Variance : – POPULATION Std. Dev. : (F.S.) Variance : – SAMPLE – The range (p. 51)  ¡ ¡ ¡ ¥ ¤ Graphical Methods:Stem/Leaf, Histograms, ¡ £ £ £ £ ¡ (p. 52) How about Variability, Spread or Dispersion? © Types of Data (p. 8): Quantitative, Qualitative ¢ STA 2023 c D.Wackerly - Review for Exam I ¥ Chapter 2 : 3 ¦ ¤  ¦ ¦ § © ¨   ¥    § ¤  ¥   ¥  ¡ STA 2023 c D.Wackerly - Review for Exam I  4 score : value mean standard deviation (p. 65) Empirical Rule (bell-shaped distns) “approx.” (p. 57) least”(p. 56) ment of how likely or probable an occurrence is. Rare Events and Inference - requires the assess- Quartiles (p. 69) Percentiles (p. 64) Miscellaneous ¡ ¡ ¡ , (p. 101) RB RW IW IB DW Intersection and Union of two events (p. 104) How to find the probability of an event (p. 106) Events (p. 105) Properties of Probabilities of Simple Events (p. 104) Sample Space, Sample Point (p. 101) Probability (p. 102) Experiment (p. 100) Chapter 3 : Tchebysheff’s Theorem (always works) “at ¡ ¡ ¡ © ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ © STA 2023 c D.Wackerly - Review for Exam I ¢ Interpreting the mean and standard deviation 5 £ STA 2023 c D.Wackerly - Review for Exam I DB ¡ 6 £ £ £ ¤ ¢ £  £ £ (2) (1) £ ¢ £ ¢  ¢ £ ¢ £   £  ¢ ¡ ¢  ¡ ¡ ¡ ¡   ¢ ¤ £ £ ¤ mutually exclusive – Put the pieces together! – – – – – £  £ (F.S.) (F.S.) (F.S.) – Altzheimers Example(like 3.109, p. 158) £   Independent (p. 131, 133):  ¦ ¢ £ ¢  ¢   ¤  ¢ ¢ ¡ and £ ¦  ¤      ¢ £ (F.S.) ¤ ¡ ¦ ¢ ¦ ¢ £ ¤ ¦ ¢  £ ¦ Multiplicative Law (p. 128) (F.S.):   ¡ £  ¢ Conditional probability (p. 122) £ ¢ ¤  ¡  ¢   £ £ ¤    ¤   ¦  ¢ £ £ ¢ £ ¦  ¦  ¢ £  ¦ £ ¦  ¢ ©   £ (F.S.) ¥ £      §¨   ¢ ¢ ¢ £   £  ¡  ¢  ¦  ¢ ¢ £ ?  ¤  ¢ ¡ What is  ¦ ¥ ¥      ¢ . ©  ¥ £ ¦   and ¢ § £   £ £  ¡  £  £  ¢   ¢ Know ¥    Additive Rule (p. 117): £ £  (F.S.) Complement (p. 115) ¡   STA 2023 c D.Wackerly - Review for Exam I £ ©     Mutually exclusive (disjoint) (p. 118) 7 ¡ STA 2023 c D.Wackerly - Review for Exam I £ 8 ¦ (p. 174). is If ¡ number of trials, ¥ Variance (p. 185) : Mean (p. 185) :  ¡ Binomial Experiment p. 179 – ¦ £ ¡ ¡ ¡ – The standard deviation of  ¢  ¦  – Variance (p. 174) (F.S.) ¦ ¦ ¦ ¡ ¡ ¨ ¦  ¡ © ¨ ¡  £¥ ¨ ©§ ¢ – Mean (p. 172) (F.S.)  © – but NOT ALL ¦  ¡  ¢ ¢   ¡ ¦ for : (p. 183) criteria SOME discrete random variables are binomial ¦ ¤ ¡ – Probability Distribution (p. 169) ¢ ¥  ¥  ¡¡ ¡   ¡ ¡ £ £ £  ¡ ¥ § ¨ ¦  ¨ ¡ ¦ Discrete Random Variables (p. 166)   £ – The Binomial Probability Distribution   ¡ ¨ §  Continuous Random Variables (p. 166)  Random Variable (p. 164)  ¥   ¡ STA 2023 c D.Wackerly - Review for Exam I  Chapter 4 : 9  STA 2023 c D.Wackerly - Review for Exam I 10 ¨ For Tuesday 10/8/02: EXAMS RETURNED For Monday: Pages 215–226 ¡ ¡ is the number of 6. Binomial Distribution 5. ¡ ¡ 99, 101, PROJECT 2 ¦ for ’s in the 4. Trials are independent.  Exercises 4.33, 37, 38, 45, 47, 49-52, 93, 95, 97,  ¡ For tomorrow: ¥ ¦ ¦ Today : Pages 185 – 189, 210–211 ¡ stays same from trial to trial.  3. Prob. of .  ¡ ¡ trials. § or ¦ Assignments  identical trials in experiment. ¦ ¨ ¡  ¦ ¢  ¡ ¡ ¨ ©§  ¡  2. Each trial results in one of two possible outcomes, 1. ¦ ¨ § ¨ ¡ © ¨   Thought: Despite the high cost of living, it’s still popular. ¨ Binomial Experiment p. 179 STA 2023 c D.Wackerly - Lecture 10 ¡ ¡ ¥ ¦   ¦ §  ¨  ¨ 133   STA 2023 c D.Wackerly - Lecture 10 134 ¨  £¢ §¦ ¡ with ? ¥ ¥ 1 ¦ 2  3 k   § ¥ ¡   ¡  0 k+1 .....        .....    be obtained from these.   ¦ ¡ ¦  §   §   ? 135 . Any needed prob. can n-1 ¡ for ¡   ¡  ¡   n  ¨ gives cumulative binomial probabilities, i.e., it gives The table of the binomial distribution (pp. 770–773)  Ex. Have a binomial variable tedious.  ¨ ¦ ¡ ¦ £¢ ¡ ¡  ¤¢ ¦  ¦ ¤  ¡ ¦ ¤¢  Computing binomial probabilities is easy but may be STA 2023 c D.Wackerly - Lecture 10 ¦ ¤ ¥ ¡   ¤¢ ¤  ¥ ¨   ¤  ¡ § ¡ ¥ ¥©  ¤    0.01 1.000 1.000 1.000 1.000 1 2 3 4 5 1.000 1.000 1.000 8 7 1.000 .996 0 6 .904 k n=10 9 ... ... ... ... ... ... ... ... ... ... ... .994 .954 .833 .618 .367 .166 .055 .012 .002 .000 0.60 p .972 .851 .617 .350 .150 .047 .011 .002 .000 .000 0.70 A Portion of Table II (p. 771) STA 2023 c D.Wackerly - Lecture 10 ... ... ... ... ... ... ... ... ... ... ... .096 .004 .000 .000 .000 .000 .000 .000 .000 .000 0.99 136 (b)  . 0 1 1 2 4 _ X<7 3 ¡ §   6 7  _ X>8 8 9 10 3 _ X<6 2 4 6 X=7 7 9 10 [from Table II] 8 £  ¦   0 1 3 _ X<4 2 4 5 _ X<8 7 __ 5<X<8 6 8 9 Lutheran, any other (or no) rel. affil.) gun owner who favors gun control, everyone else) ( favor gun control. Interested in the number who are gun owners and ( Interested in the number who are Lutherans 10 “more than 4 and no more than 8.” Ex. Conduct a survey, randomly select 10 indiv.: (c) ¢  © _ X<7 5 5 [from Table II, p. 913]  0  § : ¡ ¡  to find: ¡ (a) § bin ¥ ¡ ¡ ¡ ¡ ¢ ¡ ¢ ¡ ¥ ¡ ¢ Ex. Use the table for   ¦ ¦ ¦ ¡  ¡ ¢ ©  ¢ ©  ¤ ¡  ¢ ¥ ¡ STA 2023 c D.Wackerly - Lecture 10 ¡ ¡  ¦   ¡ ¡ ¦ ¡  ¡ ¥ ¡ ¥  £ ¦ ¦ ¦ § ¦ ¦ ¦ ¦ ¦ ¦ 137 STA 2023 c D.Wackerly - Lecture 10 ¦ 138 ¡ number of correct  # correct choices in 20 trys correct and ¨ ¡ and . . correct ? is a binomial random variable with  – ¡ ¡ – What is a “success” in this case? Let – ¡ ¡ ¡ ¡  If the psychic is guessing, what is ¦ ¦  identifications. Assume 20 trials are indep. ¦ ¥ £ £ £ £  0 1 2 3 ..... (Table II(h), p. 802)  5 6 ..... Don’t help for 140 ’s and ’s 19 20 ’s and ’s not covered in table Eliminate tedious calculations for some Advantages and Disadvantages of Tables – – What is prob. psychic is correct “6 or more times”? STA 2023 c D.Wackerly - Lecture 10 ¡ 20 times and record ¦   § Psychic tries to identify card (without looking). Do this ¡ ¡ ¡ ¡  ¡ ¡  §  § Ex. Claimed Psychic. Five cards shuffled, one chosen. ¨ ¡ ¡ ¡ ¨ ¢ ¢ ¦  ¦ ¨ ¦ ¦ ¨ 139 ¡ ¦ ¦ ¦ ¦ ¨ STA 2023 c D.Wackerly - Lecture 10 ¡ ¡ ¡ and and . ’s up to a fairly large value. Probability Distributions Binomial and ) Click in box opposite “Probability of success:”, type Click in box opposite “Number of trials:”, type in Click on radio button “Probability” Calc Start Minitab correct exactly 6 times? (recall, What is the probability that the guessing psychic is How? Works for any ¨ context of application, identify Still need to identify what a “Success” is in the ¡ ¡ interest is binomial. ¡ ¡ ¡ ¡ in Click OK Click on radio button “Input constant”, type in 6 Binomial with and Binomial with Different? Why? and Cumulative Distribution Function – “Input constant” is 5 – Click on radio button “Cumulative Probability” Just like above, except: correct 5 times or less? What is the probability that the guessing psychic is ¡ Still need to “diagnose” that the distribution of ¡ Probability Density Function  How about Minitab? ¦ ¤ ¨ STA 2023 c D.Wackerly - Lecture 10 § ¨ ¦ © ¤ ¦  ¡  141  ¡ §  ¡  ¤ ¨ ¦      STA 2023 c D.Wackerly - Lecture 10 ¤  ¡ ¡ ¡ ¡  §   ¡  §  ¡ ¡  ¡ ¡ ¥  £ ¤   ¤   ¨ §   ¡   ¡ ¦ § ¤  ¤  ¦ ¦    ¦ ¦  ¤ ¤   ¡  ¡ ¥    142 ¨ ¦ § £ £ £ £ ¡ £  ¡  and ¤¢  ¡ ¡ ¦ ¡  ¡ ¦   ¤  £¢ ¦ ¡ ¦ Minitab,   Ex. Have a binomial variable but ? £ ¡ ¡ £  ¡  Alternative–do it by hand!!! ¦ ¡ ¡ £ ¦  £  Binomial with ¦ ¨ § §   Cumulative Distribution Function , use Minitab to get §  ¨ ¡ ¤ ¤ ¡  ¤   ¡ ¡ ¥ ¦ ¡ ¦ ¨ ¦ , Can we use tables in back of book? ¤¢ ©   £ £  ¦ ¦  or more have been abused?  ¡   ¤ ¡  ¡ £ ¥ ¦  ¡ £ £ ¡ ¥ £ ¡   , ? ¡ Assign a “chunk” of prob. to each distinct value. “jumps” between the possible values. Countable number of distinct values, look for 144 histogram A mathematical model for the population (p. 210). – The “density” can be written a function of , – The depth or density depends on the value of . – It will pile up in certain places. interval like we would spread a handful of sand. Distribute our 1 unit of probability over appropriate to each Too many values go assign a “chunk” of probability etc. No gaps between values : Time, Height, Pressure, more line intervals Take on values associated with points on one or Continuous Random Variables ¡ ¡ ¡ ¡ ¡ women, what is prob. that 4  Randomly select ¡ ¡ ¥ ¦ Discrete Random Variables £  Ex. #4.47 One in three women victim of dom. abuse. ¤¢ STA 2023 c D.Wackerly - Lecture 10 ¡     ¢ 143 ¡ STA 2023 c D.Wackerly - Lecture 10 ¡ Use a table.  ¡ ¡ ¡ ¡  Calculus (not in this class) a continuous random variable, ¥  – How do I find these areas? ¡  b UNLIKE for discrete random variables, if For any single value , ¡ ¦ a value in that interval (p. 210). will take corresponds to the probability that ¢ Over a given interval, the area under the graph of ¥   ¡ Total Area = 1 ¡ Line has area 0 ¡ ¡ The area under a curve above a single point graph of f(x)   a ¡ ¡ (p. 210).  ¢ ¡ P(a<X<b) ¦ ¢ is ¡ ¦ ¥ £ ¡ b  ¢ £ graph of f(x) ¡ ¦ ¡ intervals are areas under curves:  The total area under graph of  a  ¥ § is a is 0. For a continuous random variable, Probabilities of ¢ P(a<X<b) ¡ STA 2023 c D.Wackerly - Lecture 10 ¢ graph of f(x) ¦  ¡ ¡ ¡ ¡ 145 ¢ STA 2023 c D.Wackerly - Lecture 10  ¢ 146 ...
View Full Document

Ask a homework question - tutors are online