B3102
確率
PROBABILITY 		基盤科目-データサイエンス科目-データサイエンス１
Fundamental Subjects - Subjects of Data Science - Data Science 1
2 単位
実施形態
開催日程 秋学期
担当教員 未定（ミテイ）
関連科目
開講場所 SFC
授業形態 講義
履修者制限

履修人数を制限する

受入学生数（予定）：約 50 人
2020年度秋学期開講のデータサイエンス1では、特殊な「システムによる選抜（抽選）」を行います。通りたい度は設定できず、通りたい度を設定する通常の「システムによる選抜（抽選）」にも影響しません。また、2020年度9月入学の新入生はデータサイエンス1の授業が複数許可されることがないように抽選されます。

◯エントリー〆切日時：2020年9月28日（月） 17:00
◯履修許可者発表日時：2020年9月30日（水） 17:00

Only the selected students can take this course.
Number of students in the class (scheduled) : About 50

A special "Automatic Screening (Lottery)" is applied for Data Science 1 Courses in the Fall Semester 2020. Students cannot set Course Preferences for these courses and it won't affect an ordinary "Automatic Screening (Lottery)", which students set Course Preferences. The students entered in September 2020 will not be permitted for more than one class of Data Science 1.

* Entry deadline : September 28, 2020 (Mon) 17:00
* Screening result announcement : September 30, 2020 (Wed) 17:00
履修条件

Calculus and multiple integrals.

「データサイエンス基礎」の単位を修得していること。またはデータサイエンス科目認定試験に合格していること。

In order to register the Subjects of Data Science, students need to earn credits for "Basics of Data Science" or pass the "Data Science Qualification Examination"
使用言語 英語
連絡先 miyoshih@sfc.keio.ac.jp
授業ホームページ
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設置学部・研究科 総合政策・環境情報学部
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履修選抜・課題タイプ=テキスト登録可 false
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最終更新日 2020/09/23 13:09:43

科目概要

Probability and statics are well established branches of mathematics that has applications in all areas of technology today.

This course mainly presents a solid foundation for probability and the introduction of statics, explaining its ideas and techniques necessary for a firm understanding of the topic.

授業シラバス

主題と目標／授業の手法など

Master the basic concepts associated with probability and statics.

In this course, we treat the discrete and continuous probability distribution and we use the sum and the integral. Even if you are not so familiar with the integral calculus, make the numerical formula.

In this course, we treat some kinds of probability distributions. Understand the differences and relationships of these distributions.

In this course, we will treat sampling theorem, estimation theorem, tests of hypotheses and significance.
Be familiar with the concept of these topics.

教材・参考文献

The class follows the guidelines of the book
Schaum's outlines Probability and Statistics (4th edition)
By:
Murray R. Spiegel,
John Schiller,
R. Alu Srinivasan

提出課題・試験・成績評価の方法など

The final grade of the class will be calculated as follows:
50% : Mid-term exam (or a report)
50% : Final exam (or a report)

履修上の注意

All classes will be offered on-demand.（update:9/15）
Please note that the videos of each class will be uploaded by the date listed on the syllabus. You do not have to be viewed on that date, but recommended be viewed within one week.(update:9/18)

授業計画

第1回 Basic Probability 1（10/2）

Random Experiments, Sample Spaces, Events, The Concept of Probability, The Axioms of Probability, Some Important Theorems on Probability, Assignment of Probabilities, Conditional Probability, Theorems on Conditional Probabilities

第2回 Basic Probability 2（10/9）

Independent Events, Bayes' Theorem or Rule, Combinations, Binomial Coefficients, Stirling's Approximation to n!

第3回 Random Variables and Probability Distributions 1（10/16）

Random Variables, Discrete Probability Distributions, Distribution Functions for Random Variables, Distribution Functions for Discrete Random Variables, Continuous Random Variables, Graphical Interpretations

第4回 Random Variables and Probability Distributions 2（10/23）

Joint Distributions, Independent Random Variables, Change of Variables, Probability Distributions of Functions of Random Variables, Convolutions, Conditional Distributions, Applications to Geometric Probability

第5回 Mathematical Expectation 1（10/30）

Definition of Mathematical Expectation, Functions of Random Variables, Some Theorems on Expectations, The Variance and Standard Deviation, Some Theorems on Variance, Standardized Random Variables, Moments, Moment Generating Functions, Some Theorems on Moment Generating Functions

第6回 Mathematical Expectation 2（11/6）

Characteristic Functions, Variance for Joint Distributions. Covariance, Correlation Coefficient, Conditional Expectation, Variance, and Moments, Chebyshev's Inequality, Law of Large Numbers, Other Measures of Central Tendency, Percentiles, Other Measures of Dispersion, Skewness and Kurtosis

第7回 Special Probability Distributions 1（11/13）

The Binomial Distribution, Some Properties of the Binomial Distribution, The Law of Large Numbers for Bernoulli Trails, The Normal Distribution, Some Properties of the Normal Distribution, Relation Between Binomial and Normal Distributions, The Poisson Distribution, Some Properties of the Poisson Distribution, Relation Between the Poisson and Normal Distributions

第8回 Special Probability Distributions 2（11/20）

The Central Limit Theorem, The Multinomial Distribution, The Hypergeometric Distribution, The Uniform Distribution, The Chi-Square Distribution, Student's t Distribution, The F Distribution, The Relationships Among Chi-Square, t, and F Distributions, The Bivariate Normal Distribution, Miscellaneous Distributions

第9回 Sampling Theory 1（11/27）

Population and Sample. Statistical Inference, Sampling With and Without Replacement, Random Samples. Random Numbers, Population Parameters, Sample Statistics, Sampling Distributions The Sample Mean, Sampling Distributions of Means, Sampling Distribution of Proportions, Sampling Distribution of Differences and Sums

第10回 Sampling Theory 2（12/4）

The Sample Variance, Sampling Distribution of Variances, Case Where Population Variance Is Unknown, Sampling Distribution of Ratios of Variances, Other Statistics, Frequency Distributions, Relative Frequency Distribbutions, Computation of Mean, Variance, and Moments for Grouped Data

第11回 Estimation Theory 1（12/11）

Unbaised Estimates and Efficient Estimates, Point Estimates and Interval Estimates. Reliability, Confidence Interval Estimates of Population Parameters, Confidence Intervals for Means

第12回 Estimation Theory 2（12/18）

Confidence Intervals for Proportions, Confidence Intervals for Differences and Sums, Confidence Intervals for the Variance of a Normal Distribution, Confidence Intervals for Variance Ratios, Maximum Likelihood Estimates

第13回 Test of Hypotheses and Significance 1

Statistical Decisions, Statistical Hypotheses. Null Hypotheses, Tests of Hypotheses and Significance Type I and Type II Errors, Level of SignificanceTests Involving the Normal Distribution

第14回 Test of Hypotheses and Significance 2

One-Tailed and Two-Tailed Tests, P Value, Special Tests of Significance for Large Samples, Special Tests of Significance for Small Samples, Relationship Between Estimation Theory and Hypothesis Testing

第15回 Test of Hypotheses and Significance 3

Operating Characteristic Curves. Power of a Test Quality Control Charts, Fitting Theoretical Distributions to Sample Frequency Distributions, The Chi-Square Test for Goodness of Fit, Contingency Tables, Yates' Correction for Continuity, Coefficient of Contingency

15回目に相当するその他の授業計画

Wrap-up and Final Examination