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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

bookProbability Density Function (PDF) 1/2

What is it?

We can interpret the function whose value at any given sample in the sample space as providing a relative likelihood that the value of the random variable would be close to that sample. Too simplify, it is very similar to the PMF but uses continious random variable instead of discrete.

distribution picture

Explanation:

With this probability, we have to work with a graph. Probability, in this case, is the area under the curve; hence, we can't calculate the probability of a single point because the area under it equals 0.

Example:

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Section 4. Chapter 6
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