Harvardx Data Science Professional Certificate

This repository includes my course notes, assessments, and resources from Module 3: Probability of the 17-month-long Harvardx Professional Certificate Program in Data Science.

Module 3: Data Science - Probability

What I Learned:

Section 1: Discrete Probability:

• Important concepts in probability theory including random variables and independence
• The meaning of expected values and standard errors and how to compute them in R
• Applied basic probability theory to categorical data
• Performed Monte Carlo simulations to approximate the results of repeating an experiment over and over, including simulating the outcomes in the Monty Hall problem
• Distinguished between: sampling with and without replacement, events that are and are not independent, and combinations and permutations
• Applied the multiplication and addition rules, as appropriate, to calculate the probably of multiple events occurring
• Used sapply instead of a for loop to perform element-wise operations on a function

Section 2: Continuous Probability

• Understoodd the differences between calculating probabilities for discrete and continuous data
• Used cumulative distribution functions to assign probabilities to intervals when dealing with continuous data
• Used R to generate normally distributed outcomes for use in Monte Carlo simulations
• Knew some useful theoretical continuous distributions such as normal, student-t, chi-squared, exponential, gamma, beta & beta-binomial distributions

Section 3: Random Variables, Sampling Models & Central Limit Theorem

• Understood what random variables are, how to generate them, and the correct mathematical notation to use with them
• Used sampling models to estimate characteristics of a larger population
• Explained the difference between a distribution and a probability distribution
• Understood the Central Limit Theorem, its importance, and and the law of large numbers

Section 4: The Big Short: Case Study

• Understood the relationship between sampling models and interest rates (as determined by banks)
• Understood how interest rates can be set to minimize the chances of the bank losing money
• Understood how inappropriate assumptions of independence contributed to the financial meltdown of 2007

The Harvardx Data Science Professional Certificate

Courses in this program:

1. Data Science: R Basics
2. Data Science: Visualization
3. Data Science: Probability
4. Data Science: Inference & Modeling
5. Data Science: Productivity Tools
6. Data Science: Wrangling
7. Data Science: Linear Regression
8. Data Science: Machine Learning
9. Data Science: Capstone

What I Learned:

• Fundamental R programming skills
• Statistical concepts such as probability, inference, and modeling and how to apply them in practice
• Gained experience with the tidyverse, including data visualization with ggplot2 and data wrangling with dplyr
• Became familiar with essential tools for practicing data scientists such as Unix/Linux, git and GitHub, and RStudio
• Implemeneted machine learning algorithms
• In-depth knowledge of fundamental data science concepts through motivating real-world case studies

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The course, including its assessment questions and data sets were provided by Rafael A Irizarry, Professor of Biostatistics at Harvard Chan School of Public Health and Professor of Biostatistics and Computational Biology at the Dana-Farber Cancer Institute.