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Probability Theory Update
course content

Course Content

Probability Theory Update

Probability Theory Update

1. Probability Basics
Set TheoryProbability ExperimentStatistical Independence
2. Statistical Dependence
Dependent EventsMutually Exclusive EventsAddition Rule for Mutually Exclusive EventsAddition Rule for Non-Mutually Exclusive EventsMultiplication Rule for Independent EventsMultiplication Rule for Dependent EventsConditional probabilityBayes Rule
3. Learn Crucial Terms
Random VariableDiscrete vs Continuous Random VariableExpected ValueThe Law of Large NumbersCMT
4. Probability Functions
Binomial DistributionProbability Mass Function (PMF) 1/2Probability Mass Function (PMF) 2/2Cumulative Distribution Function (CDF) 1/2Cumulative Distribution Function (CDF) 2/2Probability Density Function (PDF) 1/2Probability Density Function (PDF) 2/2
5. Distributions
Poisson Distribution 1/3Poisson Distribution 2/3Poisson Distribution 3/3Standard Normal Distribution (Gaussian distribution) 1/2

bookStatistical Independence

Independent events:

Two events are called independent if the occurrence of one doesn't affect the occurrence of the other. Example:

If you toss a coin several times, the outcome of each event doesn't depend on the other. Or real-life example: the probabilities that on Monday it will rain, and that eggs are out of stock in a grocery are independent.

Why is it so essential to understand if the probabilities are independent?

In this course, we will work with independent and dependent events. Each of them has its formulas for calculation probabilities; thus, if we can't recognize whether the probability is dependent or not, we will not be able to solve the task correctly.

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Section 1. Chapter 3
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