Data Science Statistics

Unit 1 – Intro to Probability & Stats for Data Science

Unit 2 – Probability Axioms and Bayes' Theorem

Unit 3 – Random Variables & Probability Distributions

Unit 4 – Discrete Probability Distributions

Unit 5 – Continuous Probability Distributions

Unit 6 – Joint Distributions & Independence

Unit 7 – Expectation, Variance & Covariance

Unit 8 – Sampling and Data Collection Methods

Unit 9 – Descriptive Stats & Exploratory Analysis

Unit 10 – Statistical Inference: Estimation & Intervals

Unit 11 – Hypothesis Testing & p-values

Unit 12 – Simple Linear Regression & Correlation

Unit 13 – Multiple Linear Regression & Model Selection

Unit 14 – Analysis of Variance (ANOVA)

Unit 15 – Bayesian Inference & Posterior Distributions

Unit 16 – Maximum Likelihood & Optimization

Unit 17 – Statistical Learning and Regularization

Unit 18 – Nonparametric Methods & Resampling

Unit 19 – Time Series Analysis & Forecasting

Unit 20 – Statistical Programming & Data Viz

## What do you learn in Probability and Mathematical Statistics in Data Science

You'll dive into probability theory, random variables, and statistical inference. The course covers distributions, hypothesis testing, and estimation techniques. You'll learn to apply these concepts to real-world data science problems, exploring topics like Bayesian inference, maximum likelihood estimation, and regression analysis. It's all about understanding the mathematical foundations that power data-driven decision-making.

## Is Probability and Mathematical Statistics in Data Science hard?

It can be pretty challenging, not gonna lie. The math can get intense, especially if you're not used to dealing with abstract concepts. But here's the thing: it's not impossible. Most students find it tough at first, but once things start clicking, it gets easier. The key is to stay on top of the material and practice a lot. Don't let the initial difficulty scare you off.

## Tips for taking Probability and Mathematical Statistics in Data Science in college

1. Use [Fiveable Study Guides](https://fiveable.me/cram-mode) to help you cram 🌶️
2. Practice, practice, practice - solve as many problems as you can
3. Form study groups to tackle challenging concepts together
4. Use visualization tools to understand probability distributions
5. Apply concepts to real-world scenarios (like analyzing sports stats or weather patterns)
6. Don't just memorize formulas, understand the reasoning behind them
7. Watch YouTube videos on tricky topics (3Blue1Brown has great probability explainers)
8. Use R or Python to simulate probability experiments
9. Read "The Drunkard's Walk" by Leonard Mlodinow for a fun take on probability

## Common pre-requisites for Probability and Mathematical Statistics in Data Science

1. Calculus I and II: These courses cover limits, derivatives, and integrals. They're essential for understanding probability density functions and expected values.

2. Linear Algebra: This class focuses on vector spaces, matrices, and linear transformations. It's crucial for understanding multivariate statistics and dimensionality reduction techniques.

3. Introduction to Programming: Usually in Python or R, this course teaches basic coding skills. It's important for implementing statistical algorithms and data analysis techniques.

## Classes similar to Probability and Mathematical Statistics in Data Science

1. Machine Learning: This course explores algorithms that can learn from and make predictions on data. It builds on statistical concepts to develop models for classification, regression, and clustering.

2. Bayesian Statistics: Focuses on the Bayesian approach to probability and statistics. You'll learn about prior and posterior distributions, Bayesian inference, and Markov Chain Monte Carlo methods.

3. Time Series Analysis: Covers statistical methods for analyzing time-dependent data. You'll learn about autoregressive models, forecasting techniques, and handling seasonal data.

4. Stochastic Processes: Explores random processes that evolve over time. It covers Markov chains, Poisson processes, and Brownian motion, which are crucial in modeling many real-world phenomena.

## Majors related to Probability and Mathematical Statistics in Data Science

1. Data Science: Combines statistics, computer science, and domain expertise to extract insights from data. Students learn to collect, analyze, and interpret complex datasets using advanced computational techniques.

2. Statistics: Focuses on the collection, analysis, interpretation, and presentation of data. Students develop a deep understanding of probability theory, statistical inference, and experimental design.

3. Applied Mathematics: Applies mathematical methods to solve real-world problems in science, engineering, and industry. Students learn to model complex systems and develop analytical and computational skills.

4. Computer Science: Deals with the theory, design, and application of computer systems. Students learn programming, algorithms, and data structures, often applying statistical methods in areas like machine learning and artificial intelligence.

## What can you do with a degree in Probability and Mathematical Statistics in Data Science?

1. Data Scientist: Analyzes complex datasets to extract insights and inform business decisions. They use statistical methods and machine learning algorithms to solve problems and create predictive models.

2. Quantitative Analyst: Applies mathematical and statistical methods to financial and risk management problems. They develop and implement complex models to price financial instruments and assess investment strategies.

3. Biostatistician: Applies statistical methods to biological and medical research. They design experiments, analyze clinical trial data, and help interpret results for medical professionals.

4. Machine Learning Engineer: Develops and implements machine learning models and algorithms. They work on projects like natural language processing, computer vision, and recommendation systems.

## Probability and Mathematical Statistics in Data Science FAQs

1. How much coding is involved in this course? While the focus is on mathematical concepts, you'll likely use statistical software like R or Python to implement and visualize statistical methods.

2. Can I use a graphing calculator for exams? It depends on your professor, but many allow basic calculators. Some might even permit computer use for certain parts of exams.

3. How does this course differ from a general statistics course? This course goes deeper into the mathematical foundations and typically covers more advanced topics relevant to data science applications.

4. Are there any good online resources for extra practice? Websites like Khan Academy and Coursera offer great supplementary materials on probability and statistics. Many students also find StatQuest videos on YouTube helpful for visualizing complex concepts.

Statistics

Data Science

1.1 Fundamentals of Probability and Statistics

1.2 Role of Probability and Statistics in Data Science

1.3 Basic Set Theory and Counting Principles

1.4 Introduction to Statistical Software and Tools

2.1 Probability Axioms and Properties

2.2 Conditional Probability and Independence

2.3 Bayes' Theorem and Applications

2.4 Law of Total Probability

3.1 Concept of Random Variables

3.2 Probability Mass and Density Functions

3.3 Cumulative Distribution Functions

3.4 Expected Value and Moments

4.1 Bernoulli and Binomial Distributions

4.2 Poisson and Geometric Distributions

4.3 Hypergeometric and Negative Binomial Distributions

5.1 Uniform and Normal Distributions

5.2 Exponential and Gamma Distributions

5.3 Beta and t-Distributions

5.4 Multivariate Normal Distribution

6.1 Joint, Marginal, and Conditional Distributions

6.2 Covariance and Correlation

6.3 Independence of Random Variables

7.1 Properties of Expectation and Variance

7.2 Covariance and Correlation Analysis

7.3 Moment Generating Functions

8.4 Central Limit Theorem

8.3 Sampling Distribution of the Mean

8.1 Simple Random Sampling

8.2 Stratified and Cluster Sampling

9.1 Measures of Central Tendency and Dispersion

9.2 Data Visualization Techniques

9.3 Exploratory Data Analysis Methods

10.2 Interval Estimation and Confidence Intervals

10.1 Point Estimation and Properties of Estimators

10.3 Sample Size Determination

11.4 Power Analysis

11.3 p-values and Significance Levels

11.2 Type I and Type II Errors

11.1 Null and Alternative Hypotheses

12.1 Simple Linear Regression Model

12.2 Least Squares Estimation

12.3 Model Diagnostics and Assumptions

12.4 Correlation Analysis

13.1 Multiple Linear Regression Model

13.2 Variable Selection and Model Building

13.3 Multicollinearity and Interaction Effects

13.4 Model Validation and Diagnostics

14.1 One-way ANOVA

14.2 Two-way ANOVA

14.3 ANCOVA and Repeated Measures ANOVA

15.1 Bayesian Probability and Inference

15.2 Prior and Posterior Distributions

15.3 Bayesian Estimation and Credible Intervals

15.4 Markov Chain Monte Carlo Methods

16.1 Likelihood Function and Maximum Likelihood Estimation

16.2 Properties of Maximum Likelihood Estimators

16.3 Numerical Optimization Techniques

17.1 Bias-Variance Tradeoff

17.2 Regularization Techniques (Lasso, Ridge)

17.3 Cross-validation and Model Selection

18.1 Kernel Density Estimation

18.2 Bootstrapping and Jackknife Methods

18.3 Permutation Tests

19.1 Time Series Components and Stationarity

19.2 ARIMA Models

19.3 Forecasting Techniques and Evaluation

20.1 Introduction to R or Python for Statistical Analysis

20.2 Data Manipulation and Cleaning

20.3 Advanced Data Visualization Techniques

20.4 Reproducible Research and Reporting

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