Ppt on statistics and probability pdf

AP Statistics Chapter 8 Section 2. If you want to know the number of successes in a fixed number of trials, then we have a binomial setting. If you want.

AP Statistics Chapter 8 Section 2 If you want to know the number of successes in a fixed number of trials, then we have a binomial setting. If you want to know / a 3 each time 3.Independent events 4. Variable of interest – number of rolls until a 3 occurs Yes, Geometric distribution Rule for calculating Geometric Probabilities If X has a geometric distribution with p probability of success and (1-p) of failure on each observation, the possible values of X are 1, 2, 3, …. If n is any one of these values, then/


CME12, 2012.07.04. – Rzeszów, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center.

Which series are better START HT H T HH HTT HHT P1P1 P2P2 P3P3 P4P4 P i denotes that Andrew is here and win. Gergely WintschePart III / 21 – Probability, experiments, statistic Head runs Which series are better Gergely WintschePart III / 22 – Probability, experiments, statistic Head runs Which series are better START 7 12 29/36 1/36 6/36 29/36 12 7 1/36/


14 - 1 © 2003 Pearson Prentice Hall Statistics for Business and Economics Nonparametric Statistics Chapter 14.

14 - 1 © 2003 Pearson Prentice Hall Statistics for Business and Economics Nonparametric Statistics Chapter 14 14 - 2 © 2003 Pearson Prentice Hall Learning Objectives 1.Distinguish/Test,  2 Test 14 - 5 © 2003 Pearson Prentice Hall Nonparametric Test Procedures 1.Do Not Involve Population Parameters Example: Probability Distributions, Independence Example: Probability Distributions, Independence 2.Data Measured on Any Scale Ratio or Interval Ratio or Interval Ordinal Ordinal Example: Good-Better-Best Example:/


Review. 2 Statistical modeling  “Opposite” of 1R: use all the attributes  Two assumptions: Attributes are  equally important  statistically independent.

or Gaussian probability distribution (given the class)  The probability density function for the normal distribution is defined by two parameters:  Sample mean   Standard deviation   Then the density function f(x) is 12 Statistics for weather / = 0.000136 / (0.000036 + 0. 000136) = 79.1% 14 Probability densities  Relationship between probability and density:  But: this doesn’t change calculation of a posteriori probabilities because  cancels out  Exact relationship: 15 Naïve Bayes: discussion  Na/


Math Review 1 NumbersAlgebraGeometry/ Measurement Data, Statistics, Probability Potpourri 516 X 8 =M+54=822 Ft = ____ In.Find the average 39, 47,52 Write.

,42 What is the mean of these numbers? Jana paid 50 cents for a pack of 14 baseball cards and 75 cents for a pack of 25 baseball cards. How many baseball cards did she buy? Math Review 1 NumbersAlgebraGeometry/ Measurement Data, Statistics, Probability Potpourri If Mari earns $40 a week, how much will she earn in 6 weeks? (11 _ 9) _/


Section 8.1.2 Binomial Distributions AP Statistics January 12, 2009 CASA.

Corinne makes 75% of her free throws. What is the probability of making exactly 7 of 12 free throws. binompdf(12,.75,7)=.1032 AP Statistics, Section 8.1.24 Binomial Distributions on the calculator Binomial Probabilities B(n,p) with k successes binomcdf(n,p,k) /of all adults would “agree”. What is the probability that 1520 or more of the sample “agree”. AP Statistics, Section 8.1.210 TI-83 calculator B(2500,.6) and P(X>1520) 1-binomcdf(2500,.6,1519).2131390887 AP Statistics, Section 8.1.211 Exercises 8.8-8./


“ Building Strong “ Delivering Integrated, Sustainable, Water Resources Solutions Statistics 101 Robert C. Patev NAD Regional Technical Specialist (978)

used terms Mean Standard deviation or variance Coefficient of variation Median Skewness Correlation Distributions Types Statistics “ Building Strong “ Delivering Integrated, Sustainable, Water Resources Solutions Mean –The average of a set of values –Excel command – AVERAGE Expected value –the centroid of the probability distribution on a random variable Mean and Expected Value “ Building Strong “ Delivering Integrated, Sustainable, Water Resources Solutions Variance –The average squared/


Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 7 Section 4 – Slide 1 of 11 Chapter 7 Section 4 Assessing Normality.

option under the Regression package, but the axes are linear percents (unlike MINITAB and StatCrunch) … that can be changed manually ●StatCrunch  The option Graph – QQ Plot in StatCrunch creates normal probability plots (also called QQ plots)  The StatCrunch axes are switched compared to the MINITAB axes Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 7 Section 4 – Slide 8 of 11 Chapter 7/


LIS 570 Selecting a Sample. Summary  Sampling - the process of selecting observations random; non-random probability; non-probability You don’t have.

Inferential statistics High probability that sample generally representative of the population on variables of interest Non-random Samples  Purposive  Quota  Accidental  Generalizability based on “argument” Replication Sample “like” the population Selecting a sampling method  Depends on the population  Problem and aims of the research  Existence of sampling frame Conclusion  The purpose of sampling is to select a set of elements from the population/


Inferential Statistics. Population Curve Mean Mean Group of 30.

Inferential Statistics Population Curve Mean Mean Group of 30 Population/ group mean could have occurred by chance (remember the relationship of z scores to percentile rank). 50.034.13 Probability of higher mean 15.87% (.16) Measuring Group Means Against the Sampling Distribution Sampling Distribution (n=30) 2/ you look up the cut-off value by determining the df (identifying the distribution) and then looking up on a table of “critical values” whether the difference was significant. Now you can read the/


Statistical Weights of DNA Profiles Forensic Bioinformatics (www.bioforensics.com) Dan E. Krane, Wright State University, Dayton, OH.

that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample? Mixture statistics: Combined Probability of Inclusion (CPI) or Likelihood Ratios (LR) Mixed DNA samples Put two peoples names into a mixture. How many names/. Whose might it be? Could the actual source be: Caucasian, Afro-Caribbean, or Indo-Pakistan? If it cannot be and there is no one else in the alternative suspect pool then the suspect must be the source. A suspect pool D matches/


Introduction to & Overview of Statistical & Thermal Physics

detailed consideration of molecules as individuals. 2. Is a Microscopic, statistical approach to the calculation of Macroscopic quantities. 3. Applies the methods of Probability & Statistics to Macroscopic systems with HUGE numbers of particles. Statistical Mechanics 3. For systems with known energy (Classical or Quantum) it gives BOTH A. Relations between Macroscopic quantities (like Thermo) AND B. NUMERICAL VALUES of them (like Kinetic Theory). This course/


1LREC 2010 Valletta, Malta BAStat : New Statistical Resources at the Bavarian Archive for Speech Signals Florian Schiel Bavarian Archive for Speech Signals.

standard annotation and segmentation BAStat orth. transcript / tagging Verbmobil (manually) lexicon SAM-PA (manually) phonetic segmentation MAUS (automatic) syllabification U. Reichel (automatic) 10LREC 2010 Valletta, Malta OnFocus / OffFocus } BAStat : Phone Statistic two phoneme sets: basic (52) + extended (76) including all possible vocalized /r/ diphthongs (e.g. /E6/ (‚er‘), /u:6/ (‚Uhr‘) etc.) phone probability P(phon) phone bigram probability P(phon2|phon1) position probability: word/


Section 4-2 Statistics 300: Introduction to Probability and Statistics.

Section 4-2 Statistics 300: Introduction to Probability and Statistics Probability Chapter 4 –Section 2: Fundamentals –Section 3: Addition Rule –Section 4: Multiplication Rule #1 –Section 5: Multiplication Rule #2 –Section 6: Simulating Probabilities –Section 7: Counting Fundamentals Vocabulary (Terms) –Event –Simple /number of all possible outcomes P(A) = (ways for A)/(all ways) Try this: What is the probability that I will get a 6 when I roll a die? Complementary Events The complement of event “A” consists/


TEXT STATISTICS 7 DAY 30 - 11/05/14 LING 3820 & 6820 Natural Language Processing Harry Howard Tulane University.

STATISTICS / sci fi1649412816 romance7419311514543 humor163088913 Conditions = categories, sample = modal verbs 1. # from nltk.corpus import brown 2. # from nltk.probability import ConditionalFreqDist 3. >>> cat = [news, religion, hobbies, science_fiction, romance, humor] 4. >>> mod = [can, could,/Prof. Howard, Tulane University 12 Another example  The task is to find the frequency of America and citizen in NLTKs corpus of presedential inaugural addresses: 1. >>> from nltk.corpus import inaugural 2. /


HYPOTHESIS TESTING Four Steps Statistical Significance Outcomes Sampling Distributions.

distribution. We make these probability judgments using a sampling distribution. What is a Sampling Distribution? Hypothetical Hypothetical A frequency distribution of sample statistics from an infinite number of samples. A frequency distribution of sample statistics from an infinite number of samples. Imagining a Sampling Distribution 1.Take a random sample. 2.Compute the mean. 3.Take another random sample and compute the mean. 4/


AP Statistics Linear Regression Inference Hypothesis Tests: Slopes Given: Observed slope relating Education to Job Prestige = 2.47 Question: Can we generalize.

Answer: Estimates of a slope (b) have a sampling distribution, like any other statistic – It is the distribution of every value of the slope, based on all /then the sampling distribution would center at zero – Since the sampling distribution is a probability distribution, we can identify the likely values of b if the population slope is/ Assumptions Normality: Examine sub-samples at different values of X. Make histograms and check for normality. Good Not very good Bivariate Regression Assumptions 4. The /


10 - 1 © 2001 Prentice-Hall, Inc. Statistics for Business and Economics Simple Linear Regression Chapter 10.

10 - 1 © 2001 Prentice-Hall, Inc. Statistics for Business and Economics Simple Linear Regression Chapter 10 10 - 2 © 2001 Prentice-Hall, Inc. Learning Objectives / Prediction & Estimation 10 - 11 © 2001 Prentice-Hall, Inc. Regression Modeling Steps 1.Hypothesize Deterministic Component 2.Estimate Unknown Model Parameters 3.Specify Probability Distribution of Random Error Term Estimate Standard Deviation of Error Estimate Standard Deviation of Error 4.Evaluate Model 5.Use Model for Prediction & Estimation 10 /


1 Chapter 4. Section 4-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman M ARIO F. T RIOLA E IGHTH E DITION E LEMENTARY.

0.002 0.000 P( x ) x Table A-1 Binomial Probability Distribution For n = 15 and p = 0.10 Method 2 9 Chapter 4. Section 4-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Example: Using Table A/is limited because a table may not be available for every n and/or p. Method 2 – Using a table 10 Chapter 4. Section 4-3. Triola, Elementary Statistics, Eighth Edition. Copyright 2001. Addison Wesley Longman Probabilities with “Exact” successes Press 2 nd, VARS (DISTR). Select /


A SAS Macro to Calculate the C-statistic Bill O’Brien BCBSMA SAS Users Group March 10, 2015.

known as discrimination, has been well studied and quantified for binary outcomes using measures such as the estimated area under the Receiver Operating Characteristics (ROC) curve (AUC), which is also referred to as a “C-statistic” (Uno 2011) data Admissions; length /non- event % of time model discriminated correctly Result c 0.72 There is a 0.72 probability of the model assigning a higher predicted probability to a randomly selected event case, compared with a randomly selected non-event case. 0.50 /


Sampling Distributions. Sampling Distribution Is the Theoretical probability distribution of a sample statistic Is the Theoretical probability distribution.

Distributions Sampling Distribution Is the Theoretical probability distribution of a sample statistic Is the Theoretical probability distribution of a sample statistic A sample statistic is a random variable: A sample statistic is a random variable: E.g/ possess characteristic Sampling Distribution of a Sample Proportion Approximated by normal distribution if: Approximated by normal distribution if: and and Mean of samples: Mean of samples: Standard error of proportion : Standard error of proportion : p = /


Lina Zhou, Member, IEEE, Yongmei Shi, and Dongsong Zhang 報告者:黃烱育 2015/11/231 碩研資工一甲 M97G0217 黃烱育.

Shi, and Dongsong Zhang 報告者:黃烱育 2015/11/231 碩研資工一甲 M97G0217 黃烱育 Outline Introduction Statistical Language Models Data Sets Discussion Conclusion 2015/11/232 碩研資工一甲 M97G0217 黃烱育 Introduction There is a growing need develop effective ways to detect online deception. That developing SLMs does not require an explicit feature selection process. 2015/11/233 碩研資工一甲 M97G0217 黃烱育 Statistical Language Models(1) n-gram models Predicting the next word by the probability function/


© 2013 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems Introductory Statistics: Exploring the World through.

For use with Classroom Response Systems Introductory Statistics: Exploring the World through Data, 1e by Gould and Ryan Chapter 9: Inferring Population Means Slide 9 - 1 If the conditions fail to be met for a hypothesis test, the z-statistic will not follow a Normal distribution when/2013 Pearson Education, Inc. Response Counter True or False A sampling distribution is a probability distribution of a statistic. A. True B. False Slide 9 - 7 © 2013 Pearson Education, Inc. Response Counter True or False When a/


ChE 452 Lecture 07 Statistical Tests Of Rate Equations 1.

To Tell If the Difference Is Statistically Significant We want to do a statistical test to calculate the probability that one model fits better than another 9 Using An F-Test To Tell If the Difference Is Statistically Significant 10 Method: Compute F inverse/ does not mean rate equation is correct. The quality of kinetic data vary with the equipment used and the method of temperature measurement and control. Data taken on one apparatus is often not directly comparable to data taken on different apparatus./


Beginning of the chapter Simple disease risk statistics 16.

Beginning of the chapter Simple disease risk statistics 16 GENETICS Disease risk statistics GENETICS How do we know the risk? Concept: Odds Ratio The risk of developing a disease due to a genetic variation Example: G = /0.6OR 1.4 3 x 0.36 x 0.6 = 0.64 OR Disease probability 13.46% 3 x 1.4 = 4.2 OR Disease probability 60.82% Disease probability average: 20% GENETICS Summary: The genetic risk is stable and unchangeable. Different analyses of the same genes should yield the same OR, even when conducted/


STATISTICSProbability Distribution” 8.0 Counting Principles & Probability Distribution.

Probability Distribution Probability Distribution 1.A probability distribution is a listing of all the possible outcomes of an experiment along with the relative frequency/probability of each outcome. 2.Probability distribution play a major role in the use of inferential statistics. 8.0 Probability Distribution Discrete Probability/: 8.0 Probability Distribution (x i )Freq 025 1185 2137 398 445 510 a) Develop a probability distribution for this data b) Calculate the mean, variance and standard deviation. /


Chapter 1: Introduction to Statistical Methods

N is even, so is m. A Fundamental Assumption is that successive steps are statistically independent Let p ≡ the probability of stepping to the right and q = 1 – p ≡ the probability of stepping to the left. Since each step is statistically independent, the probability of a given sequence of n1 steps to the right followed by n2 steps to the left is given by multiplying the/


CHAPTER 8: Sampling Distributions

Group Sampling Distribution of the Proportion When the sample statistic is generated by a count not a measurement, the proportion of successes in a sample of n trials is p, where Shape: Whenever both n p and n(1 – p) are greater than or equal/ claims that 55% of registered voters favor the candidate over her strongest opponent. Assuming that this claim is true, what is the probability that in a simple random sample of 300 voters, at least 60% would favor the candidate over her strongest opponent? p = 0/


REVIEW OF BASICS PART II Probability Distributions Confidence Intervals Statistical Significance.

REVIEW OF BASICS PART II Probability Distributions Confidence Intervals Statistical Significance Probability Distributions Probabilities are relative frequencies Probabilities vary between 0 and 1 MEAN +1SD+2SD-1SD-2SD 68% 95% +3SD-3SD 99% z - SCORES z-score: standard score measuring in units of standard deviations standard normal distribution: normal distribution in z-/


Precipitation Statistics! What are the chances?. Weather service collects precipitation data around the country.

Statistics! What are the chances? Weather service collects precipitation data around the country Burlington Data (values in inches) How can you describe? TAKE MEAN= AVERAGE(##:##) 29.51.8 TAKE MEDIAN= MEDIAN(##:##) 26.31.9 STANDARD DEVIATION = STDEV(##:##) 4.10.9 % STANDARD DEVIATION = STDEV/MEAN*100 14% 47% MAXIMUM = MAX(##:##) 2.7 34.1 MINIMUM= MIN(##:##) 0.925.8 Probability/ on probability paper Extreme values +1  84% 50th percentile, median and mean if distribution is “normal” -1  1 Standard Deviation /


PROBABILITY REVIEW PART 5 PROBABILITY FOR TEXT ANALYTICS Thomas Tiahrt, MA, PhD CSC492 – Advanced Text Analytics.

Value Sum 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Outcome Count Histogram 8 Event Probability Histogram 9 Probabilities of a Loaded Die 10 OutcomeProbability {1}1/8 {2}1/16 {3}1/8 {4}1/16 {5}1/1281/2561/16 Total1/81/161/81/161/81/163/81/161 Probabilities from Rolling Two Loaded Eight-sided Dice Event Probability Histogram 12 References 13 Sources: Foundations of Statistical Natural Language Processing, by Christopher Manning and Hinrich Schütze The MIT Press Discrete Mathematics with Applications, by /


T-Test: Statistical Analysis. What is a t-Test? Statistical test used in hypothesis testing –Example: Comparing Group A to Group B Used to determine if.

a t-Test? Statistical test used in hypothesis testing –Example: Comparing Group A to Group B Used to determine if the difference between 2 mean values is significantly different or just difference due to random chance –Example: Compare the mean between Per. 2 and Per. 3 / value: 2.101 & Calculated t-value:.33; this calculated t-value is lower than the critical t-value 2c) What is the probability that the difference between the two groups is due to chance? 50% Let’s do # 6 from Part 2 6) When comparing the/


Psyc 235: Introduction to Statistics To get credit for attending this lecture: SIGN THE SIGN-IN SHEET

: aim for 18 hours spent by the end of this week Jan 30th Target Date for Descriptive Statistics Watch videos: 1.Picturing Distributions 2.Describing Distributions 3.Normal Distributions Quiz 1 NOT GRADED available starting /, 2nd, 3rd) and order a 3-item combo plate. How many different ways can this happen? Calculating Probabilities Counting rules (Permutation, Combination, Multiplication):  Define sample space (# possible outcomes) Probability of a specific outcome: 1 sample space Probability of an event?/


Well-conditioned computation of probability densities for metastable conformations Marcus Weber Konrad-Zuse-Zentrum für Informationstechnik Berlin Computational.

atom in a 2d-plane T ¿ 4 Example: Epigallocatechine A. Fischer, Ch. Schütte, P. Deuflhard, and F. Cordes (2000) 5 Sampling Scheme q 1 T ¿ T ¿ T ¿ … q 2 q 3 q/A ( q ) ¼ ( q ) d q ­ = C 1 [ ::: [ C N 10 ZIBgridfree M. Weber (2006) adaptive sampling (hierarchical) curse of dimensionality 11 Transition Probabilities © 1 ;:::; © N : ­ ! [ 0 ; 1 ] N P i = 1 © i ( q ) = 1 ; 8 q 2 ­ P ( i ; j/= 1 A ( q ( l ) k ) statistical weights w w > = w > P Learn more about transition matrices in the talk by Susanna Kube on /


SAMPLING DISTRIBUTION. The sampling distribution is the probability distribution of a statistic based on a random sample. It is the distribution of the.

range or standard deviation etc. If a sample of size n is being taken from the population, then the statistic is calculated for all the possible samples of size n. The probability distribution is then found. Example 1: A bag contains a large number of coins. 70% are 2p coins /arrangements) 5, 5, 5 P( sample contains three 2p coins) = 0.7 3 = P( sample contains two 2p coins and one 5p) =0.7 2 × 0.3 × 3 = P( sample contains one 2p and two 5p coins) = 0.7 × 0.3 2 × 3 = P( sample contains three 5p coins) =0.3 3/


AP Statistics: Chapter 8 Intro.. You come to class totally unprepared for a quiz (imagine that!!!). The quiz consists of 10 multiple choice questions.

AP Statistics: Chapter 8 Intro. You come to class totally unprepared for a quiz (imagine that!!!). The quiz consists of 10 multiple choice questions with 5 possible answers. Since you/question correct) = _______ How many questions would you expect to get correct? _______ Let the random variable X represent the number of questions you get correct and complete this probability distribution. To find the probabilities, let’s do a simulation: Each of you do 10 simulations. 0 1 2 3 4 5 6 7 8 9 10 We can also find /


STATISTIC & INFORMATION THEORY (CSNB134) MODULE 7B PROBABILITY DISTRIBUTIONS FOR RANDOM VARIABLES ( POISSON DISTRIBUTION)

an average of  such events can be expected to occur. The probability of k occurrences of this event is For values of k = 0, 1, 2, … The mean and standard deviation of the Poisson random variable are Mean:  Standard /would be very unusual (small probability) since x = 8 lies standard deviations above the mean. This would be very unusual (small probability) since x = 8 lies standard deviations above the mean. STATISTIC & INFORMATION THEORY (CSNB134) PROBABILITY DISTRIBUTIONS OF RANDOM VARIABLES (POISSON/


Chapter 31Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

& Sons, Inc. The Box Plot (or Box-and-Whisker Plot) Chapter 313Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Comparative Box Plots Chapter 314Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Probability Distributions Chapter 315Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery/


250 trials 350 trials Probability: Relative Frequency An estimate of the probability of an event happening can be obtained by looking back at experimental.

250 trials 350 trials Probability: Relative Frequency An estimate of the probability of an event happening can be obtained by looking back at experimental or statistical data to obtain relative frequency. ColourfreqRelative freq Red50 Blue80 Green30 White40 Silver130 Black20 956 /discs. Rebecca selects a disc at random from the bag, notes its colour, then replaces it. She does this 500 times and her results are recorded in the table below. Rebecca hands the bag to Peter who is going to select one disc from /


1 Making a Big Change: Teaching Math  Teaching Statistics Daren Starnes Mathematics Department Chair The Lawrenceville School.

sources of bias –Scope of inference: random sampling vs. random assignment 9 What math teachers like 10 What statistics teachers like Using simulations to estimate probabilities 11 Finding common ground? Suppose that one percent of the women in a certain region have breast cancer. For/ Total 1000 10990 9 89 98 9/98 = 0.092 What did it for me? APES/Stats –Field study work in forests and streams –Playing the role of data consultant 15 The data are trying to tell us a story… Son #1: The firefighter –Call/


Statistics in Bioinformatics May 2, 2002 Quiz-15 min Learning objectives-Understand equally likely outcomes, Counting techniques (Example, genetic code,

have been obtained by random chance? Part of this comes from scientific intuition but another part comes from statistics. Types of statistics used in bioinformatics Yes-Likelihood methods No-ANOVA, regression analysis, hypothesis testing When one performs a sequence /are the sources of error for this approach? How to compute relevant probabilities? 1)Obtain all sequences of known DNA binders. Check for The particular aa sequence and compute its percentage. P(aa sequence/DNA binder)= # of protein with/


Using statistics in small-scale language education research Jean Turner © Taylor & Francis 2014.

11th13 © Taylor & Francis 2014  Mean = 11.14286  Median = 13  Mode = 13 and 15  Range = 11 points  Standard deviation = 3.42927 © Taylor & Francis 2014  The descriptive statistics give a sense of... ◦ central tendency ◦ dispersion  The histogram gives a sense of... ◦ the/ 0.958, p-value = 0.7225 © Taylor & Francis 2014  The observed value of the Shapiro–Wilk statistic is: W = 0.958  The exact probability of the observed value, W = 0.958, is: p-value = 0.7225 © Taylor & Francis 2014 I’m reminding /


Statistical model for count data Speaker : Tzu-Chun Lo Advisor : Yao-Ting Huang.

approximation Conclusion Statistics model A statistical model is a probability distribution constructed to enable inferences to be drawn or decisions made from data. Population sample Inference Make a decision : Hypothesis testing designer consumer We have to choose a statistics model for /negative integer values {0, 1, 2, 3,...}, and where these integers arise from counting rather than ranking. We tend to use fixed fractions of genes. The probability that reads appeared in this region The number of read/


Statistics for Business and Economics

reject the hypothesis that  = 50. ... if in fact this were the population mean Level of Significance Probability Defines unlikely values of sample statistic if null hypothesis is true Called rejection region of sampling distribution Designated (alpha) Typical values are .01,/the average capacity of batteries at least 140 ampere-hours? A random sample of 20 batteries had a mean of 138.47 and a standard deviation of 2.66. Assume a normal distribution. Test at the .05 level of significance. One-Tailed t Test/


Algebraic Statistics for Computational Biology Lior Pachter and Bernd Sturmfels Ch.5: Parametric Inference R. Mihaescu Παρουσίαση: Aγγελίνα Βιδάλη Αλγεβρικοί.

Algebraic Statistics for Computational Biology Lior Pachter and Bernd Sturmfels Ch.5: Parametric Inference R. Mihaescu Παρουσίαση: Aγγελίνα Βιδάλη Αλγεβρικοί & Γεωμετρικοί Αλγόριθμοι στη Μοριακή Βιολογία /probabilities Viterbi algorithm problem of computing p σ Tropicalization:u ij =-log(p’ ij )v ij =-log(p ij ) We can now efficiently find an explanation h 1,…,h m for the observation σ 1,…,σ n using the recursion: It is again the Forward algorithm. Pair Hidden Markov Model (pHMM) The algebraic statistical/


Chapter 4: Probability (Cont.) In this handout: Total probability rule Bayes’ rule Random sampling from finite population Rule of combinations.

How many distinct 4-person teams can be chosen? Random sampling from finite population Example(cont.):  The probability that students A,B,C,D are chosen to work on the project is 1/330.  Suppose the group consists of 5 juniors and 6 seniors. How many samples of 4 have exactly 3 juniors? Think of selecting a sample as a 2/ = (# of samples with only good cars) = C(37,4)=66,045 Thus, (# of samples with ≥1 defective cars) = 91,390 – 66,045 = 25,345 Figure 4.4 (p. 157) Probability versus statistical inference.


Statistics in Bioinformatics May 12, 2005 Quiz 3-on May 12 Learning objectives-Understand equally likely outcomes, counting techniques (Example, genetic.

of statistics typically used in bioinformatics Yes-Likelihood methods No-ANOVA, regression analysis, hypothesis testing When one performs a sequence comparison search one must ask what is the likelihood that one would obtain a match based on random chance. This depends on the sequence you are searching for and the amount of data within the database you are mining. Equally likely outcomes/


PROBABILITY REVIEW PART 4 PROBABILITY FOR TEXT ANALYTICS Thomas Tiahrt, MA, PhD CSC492 – Advanced Text Analytics.

}1/8 {5}1/8 {6}1/8 {7}1/8 {8}1/8 Examples of Marginal Probabilities 8 Complementary Probabilities 9 Outcome {1} {2} {3} {4} {5} {6} {7} {8} Complementary Examples 10 References 11 Sources: Foundations of Statistical Natural Language Processing, by Christopher Manning and Hinrich Schütze The MIT Press Discrete Mathematics with Applications, by Susanna S. Epp Brooks/Cole, Cengage/


Probability Distributions 2014/04/07 Maiko Narahara

pnorm(q=0, mean=0, sd=1) gives the cumulative probability for the given value of x How to compute p value Z-test statistic: 2.5 pnorm(2.5, lower.tail=FALSE) *note: one-tail test Cumulative probability X qnorm qnorm(0.975) returns x that corresponds to the/two-tail). Cumulative probability X Tips 1 Handling vectors rnorm(10, mean=1:10, sd=1:10) rnorm(5, mean=c(1, 1, 2, 2, 2)) – # sampling from different distributions dnorm(0, mean=1:2) dnorm(c(0, 1), mean=1:2) – # similarly, qnorm and pnorm can handle /


Ch2: Probability Theory Some basics Definition of Probability Characteristics of Probability Distributions Descriptive statistics.

1. Some Basics A random experiment Population and Sample point An event Mutually exclusive and equally likely Random variable: r.v. for short  An example: coin tossing 2. Definition of Probability The classical definition The empirical definition Absolute frequency vs. relative frequency 2. Definition of Probability (continued) Probability distribution function (PDF) Joint probability Unconditional probability vs. conditional probability Statistical independence Independence vs. non-correlation 3/


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