Week 1 - Introduction to Probability and Probability Distributions-Lesson 1 - Introduction to Probability
Course Introduction
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Check your knowledge
What is Probability?
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What is Probability? - Dice Example
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Interactive Tool: Repeated Experiments
Complement of Probability
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Sum of Probabilities (Disjoint Events)
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Sum of Probabilities (Joint Events)
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Independence
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Birthday problem
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Conditional Probability - Part 1
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Conditional Probability - Part 2
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Bayes Theorem - Intuition
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Bayes Theorem - Mathematical Formula
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Bayes Theorem - Spam example
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Bayes Theorem - Prior and Posterior
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Bayes Theorem - The Naive Bayes Model
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Probability in Machine Learning
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Week 1 - Introduction to Probability and Probability Distributions-Lesson 2 - Probability Distributions
Random Variables
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Probability Distributions (Discrete)
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Binomial Distribution
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(Optional) Binomial Coefficient
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Bernoulli Distribution
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Probability Distributions (Continuous)
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Probability Density Function
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Cumulative Distribution Function
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Interactive Tool: Relationship between PMF/PDF and CDF of some distributions
Uniform Distribution
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Normal Distribution
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(Optional) Chi-Squared Distribution
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Sampling from a Distribution
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Week 1 - Conclusion
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Week 1 - Slides
Week 1 - Introduction to Probability and Probability Distributions-Programming Assignment - Probability Distributions
(Optional) Common Coursera Labs Operations
(Optional) Assignment Troubleshooting Tips
(Optional) Partial Grading for Assignments
Week 2 - Describing probability distributions and probability distributions with multiple variables-Lesson 1 - Describing Distributions
Measures of Central Tendency
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Expected Value
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Expected value of a Function
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Sum of expectations
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Variance
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Standard Deviation
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Sum of Gaussians
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Standardizing a Distribution
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Interactive Tool: Mean, median and standard deviation
Skewness and Kurtosis: Moments of a Distribution
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Skewness and Kurtosis - Skewness
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Skewness and Kurtosis - Kurtosis
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Quantiles and Box-Plots
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Visualizing data: Box-Plots
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Visualizing data: Kernel density estimation
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Visualizing data: Violin Plots
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Visualizing data: QQ plots
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Week 2 - Describing probability distributions and probability distributions with multiple variables-Lesson 2 - Probability Distributions with Multiple Variables
Joint Distribution (Discrete) - Part 1
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Joint Distribution (Discrete) - Part 2
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Joint Distribution (Continuous)
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Marginal and Conditional Distribution
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Conditional Distribution
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Covariance of a Dataset
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Covariance of a Probability Distribution
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Covariance Matrix
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Correlation Coefficient
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Multivariate Gaussian Distribution
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Week 2 - Conclusion
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Week 2 - Slides
Week 3 - Sampling and Point estimation-Lesson 1 - Population and Sample
Population and Sample
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Sample Mean
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Sample Proportion
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Sample Variance
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Law of Large Numbers
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Central Limit Theorem - Discrete Random Variable
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Central Limit Theorem - Continuous Random Variable
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Week 3 - Sampling and Point estimation-Lesson 2 - Point Estimation
Point Estimation
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Maximum Likelihood Estimation: Motivation
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MLE: Bernoulli Example
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MLE: Gaussian Example
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MLE for Gaussian population
Interactive Tool: Likelihood Functions
MLE: Linear Regression
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Regularization
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Back to "Bayesics"
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Bayesian inference and MAP
Relationship between MAP, MLE and Regularization
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Week 3 - Conclusion
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Week 3 - Slides
Week 4 - Confidence Intervals and Hypothesis testing-Lesson 1 - Confidence Intervals
Z Distribution
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Margin of Error
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Interactive Tool: Confidence Intervals
Calculation Steps
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Confidence Interval - Example
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Calculating Sample Size
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Difference Between Confidence and Probability
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Unknown Standard Deviation
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Confidence Intervals for Proportion
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Week 4 - Confidence Intervals and Hypothesis testing-Lesson 2 - Hypothesis Testing
Defining Hypothesis
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Type I and Type II errors
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Right-Tailed, Left-Tailed, and Two-Tailed Tests
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p-Value
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Critical Values
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Power of a Test
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Interpreting Results
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t-Distribution
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t-Tests
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Test for proportions
Two Sample t-Test
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Two sample test for proportions
Paired t-Test
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ML Application: A/B Testing
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Week 4 - Conclusion
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Week 4 - Slides
Week 4 - Confidence Intervals and Hypothesis testing-End of access to Lab Notebooks
[IMPORTANT] Reminder about end of access to Lab Notebooks
Week 4 - Confidence Intervals and Hypothesis testing-Acknowledgments & Course Resources
Acknowledgments
(Optional) Opportunity to Mentor Other Learners
References