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# Probability and Statistics

##### Course Outline

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I. Introduction to Probability and Statistics
A. Importance and Applications of Probability and Statistics
B. Basic Terminology in Statistics
C. Overview of Data Types and Levels of Measurement
D. Introduction to Statistical Software

II. Descriptive Statistics
A. Measures of Central Tendency
1. Mean
2. Median
3. Mode
B. Measures of Dispersion
1. Range
2. Variance
3. Standard Deviation
C. Measures of Position
1. Quartiles
2. Percentiles
3. Z-scores
D. Data Visualization
1. Histograms
2. Box Plots
3. Scatterplots

III. Probability Theory
A. Probability Axioms and Properties
B. Counting Techniques (Permutations, Combinations)
C. Conditional Probability and Independence
D. Bayes' Theorem

IV. Random Variables and Probability Distribution
A. Discrete Random Variables
1. Probability Mass Function
2. Cumulative Distribution Function
3. Common Discrete Distributions (e.g., Binomial, Poisson)
B. Continuous Random Variables
1. Probability Density Function
2. Cumulative Distribution Function
3. Common Continuous Distributions (e.g., Uniform, Normal, Exponential)

V. Sampling Distributions and Estimation
A. Central Limit Theorem
B. Sampling Distribution of the Mean
C. Point Estimation
D. Interval Estimation
E. Confidence Intervals

VI. Hypothesis Testing
A. Basics of Hypothesis Testing
B. Type I and Type II Errors
C. One-Sample Tests
D. Two-Sample Tests
E. Tests for Proportions

VII. Correlation and Regression
A. Correlation Coefficients
B. Simple Linear Regression
C. Multiple Linear Regression
D. Goodness of Fit and Model Assumptions
E. Prediction and Confidence Intervals in Regression

VIII. Analysis of Variance (ANOVA)
A. One-Way ANOVA
B. Two-Way ANOVA
C. Post-Hoc Tests
IX. Non-parametric Statistics
A. Chi-Square Tests
B. Mann-Whitney U Test
C. Kruskal-Wallis Test
D. Spearman Correlation

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Textbook: "Probability & Statistics for Engineers & Scientists" by Ronald E. Walpole.

##### I. Introduction to Probability and Statistics

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The aim of this initial unit is to introduce students to the fundamental concepts and terminology of Probability and Statistics. It provides an overview of data types and statistical software frequently used in statistical analysis.

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A. Importance and Applications of Probability and Statistics

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Defining Probability and Statistics: Probability refers to the study of uncertainty and the likelihood of certain outcomes, while Statistics is the discipline that deals with the collection, analysis, interpretation, presentation, and organization of data.

Importance and Applications: Discuss the relevance of probability and statistics in various fields such as Computer Science, Data Science, Engineering, Medicine, and Economics. For example, in Computer Science, statistical algorithms are used in machine learning and AI to make predictions and decisions.
Real-life examples: Discuss practical examples like forecasting weather using historical data (statistics), predicting the outcome of a coin toss (probability), or using demographic data to predict customer behavior in business (both).

B. Basic Terminology in Statistics

• Population: The entire group of individuals or instances about whom we're interested in drawing conclusions.

• Sample: A subset of the population that we collect data from.

• Variable: A characteristic or attribute that can assume different values.

• Data: The values that the variables can assume.

• Parameter: A value, usually numerical, that describes a characteristic of a population.

• Statistic: A value, usually numerical, that describes a characteristic of a sample.

C. Overview of Data Types and Levels of Measurement

Levels of measurement: These are the different ways numbers or categories of a variable can be classified.
Nominal: These are categorical data and do not have an order or priority. For example, types of cuisine (Italian, Chinese, Indian, etc.).

Ordinal: These are also categorical data, but they have an order. For example, customer satisfaction level (unsatisfied, neutral, satisfied).

Interval: Numerical values where we know the order and the exact differences between the values. However, there's no "true zero". For example, temperature in Celsius (0°C does not mean the absence of temperature).

Ratio: Like interval data, but they do have a "true zero". For example, weight (0kg means the absence of weight).

Understanding scales of measurement: Discussion on how different types of data require different statistical techniques.

D. Introduction to Statistical Software

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Overview of popular statistical software: Brief introduction to tools like R (a programming language and free software environment for statistical computing), Python (with libraries like NumPy, pandas, and matplotlib for statistical analysis), and SPSS (a powerful statistical software by IBM).

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