Lecture 12: History of Life on Earth
Lecture 12: History of Life on Earth BIO 209L-001
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This 5 page Class Notes was uploaded by Kiara Reyes on Saturday September 26, 2015. The Class Notes belongs to BIO 209L-001 at Northern Illinois University taught by Dr. Renee Kopulos in Summer 2015. Since its upload, it has received 22 views. For similar materials see Human Anatomy and Physiology I Lab - SL in Biological Sciences at Northern Illinois University.
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Date Created: 09/26/15
STATS 301 Study Guide Chapter 1 Introduction to Statistics 0 Descriptive Statistics To summarize and describe the data at hand EX Sample Data Graphs Numbers Inferential Statistics Analyze small speci c set of data in order to draw a conclusion about large more general group EX Random samples Population v Population Entire collection of individual or things to be considered or evaluated Other Phrase looking at the Whole picture v Sample Small selection in individual or things taken from the population Other term sample piece v Variable Characteristic of an individual or thing in a population of interest Other words single individual reason v Sample Random Sample SRS of size n Sample selected in such a way that every possible sample of size n has the same chance of being selected Other words sample selected has same chance Chapter 2 Tables and Graphs of Summarizing Data Univariate Data 1 observation from individual or object EX Height of each person Bivariate Data 2 observation from each individual or object EX Height Weight of each person Multivariate Data 3 or more observation EX HeightWeightGenderBlood Preassure etc from each person Types of Data Categorical or Qualitative nonnumerical observation that may be placed in categories Numerical or Quantitative observations that are numbers Numerical Data is 1 Discrete set of possible values is nite set or countably in nite set EX in nite sequence with lst value 2nd value Usually associated with counting the numbers of 2 Continuous set of possible values in an in nite set that forms an interval of the number line EX Usually associated with measuring Chapter 3 Numerical Summary Measure Measure of Center Sample Mean average 5 0 Sample Median Middle 352 0 Sample Mode M Measure of Spread Empirical Rule Applies only when the shape of distribution is approximately normal Bell Shape Approximately 68 of observation Within 1 standard deviation of mean Approximately 95 of observation Within 2 standard deviation of mean Approximately 997 of observation Within 3 standard deviation of mean l I II f 5a r Chebyshev s Rule iai g r fl aMigrantHillifii lEQ lE f mlg zliz tfi aaaaa quotquot quot 39quotJquot quot quotquot u m r quot 39 39 39quot a 39 W HfquotH g a u 39 a quotquot 39 quotquotquot39I quotzEl quotk39QQquotET quotquot 39 quot 39 39 quotj quot I T quot f g39v f 50 3 1531luthi 2Il m r im iii n g i CZL3SJ ETZQ Chapter 4 Probability Experiment any activity that has at least two possible outcomes and the result of the activity cannot be predicted with absolute certainty Sample space S the set of all the possible outcomes from an experiment Simple Letters or Numbers Probability 0Complement Rule PA39 1 PA Addition Rule PA U B PA PB PA n B Addition Rule for Two Disjoint Events PA U B PA PB 0Conditional Probability If PB gt 0 then Multiplication Rule PA n B PABPB Multiplication Rule for Independent Events PA n B PAPB Chapter 5 Random Variables and Discrete Probability Distributions Random Variable a rule that assigns a unique numerical value to each outcome in a sample space typically named X Y etc Notation pX the amount of probability assigned to the speci c value X PXX EX p2 the amount of probability assigned to the speci c value 2 PX2 Section 53 Mean Variance and Standard Deviation for a Discrete RV Important summaries if a data set are Sample mean X indicates center of data Sample standard deviation S amount of spread among the data Likewise random deviation variable or probability distribution has similar summaries De nition Let X be a discrete random variable with probability mass function as shown as below andkeep inmind the Notesw W i v if I quot 39 5quot J v fie t V y 5 7 39 an t Hr gquot A fill 3947 a 39amp39 Lr u a Lirm 7 ral ff till 3 lJ1 H H I 1 m Liff r 1 quotxg J 39 n l u I39 H Section 54Binomial Distribution I Binomial Distribution any eXperiment or situation that satis es the following 1 There a known number of trials denoted by n 9 How many times you re doing something n 2 Each trail result in a success or failure 9 Identify success or fail 3 Psuccess in the same for each trail denoted by n 9 What happens to one trail happens to other trails Identical 4 The trials are independent That is the outcome of one trail will not in uence or affect the outcome of another trail Note The values of quotnquot and quotpquot are called Parameters of the Binomial experiment Binomial Random Variable X the total number of success observed during a Binomial experiment Possible values ofX are 0 1 2 3 n Binomial Probability Mass Function XBin n p mean that X is a Binomial random variable with parameters n and p px the probability of obtaining exactly x successes among the n trails Binomial Mean Variance and Standard Deviation If XBin n p then
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