Project Autodidact
Project Details: https://insightsbyse.com/projectautodidact/
Scott Ernst Bio: https://insightsbyse.com/aboutscotternst/
Project Contact: InsightsBySE@protonmail.com
Progress Report Scope (S01-M02-D02-AllParts)
Stage 1 of 4: Review of Mathematics, Probability, and Statistics
Module 2 of 3: Statistics, Probability, and Advanced Algebra
Day 2 of 5: Probability Basics
Parts 1 through 10: See below
Summary Of Goals Achieved
- Reviewed definitions, notation, terminology, components, concepts, properties, and applicability of four main types of probability (classical, empirical, subjective, and axiomatic). NOTE: Non-probabilistic uncertainty methods (fuzzy logic, possibility theory, Dempster-Shafer theory, and info-gap decision theory) will be subsequently studied in more detail.
- Reviewed definitions, notation, terminology, and components of fundamental axioms of probability (non-negativity, normalization, and additivity)
- Reviewed definitions, notation, terminology, and components of fundamental rules of probability (complement rule, addition rule for non-mutually exclusive events, conditional probability, multiplication rule, and law of total probability)
- Reviewed methods for calculating marginal probability of a single event (aka unconditional, simple, or basic probability)
- Reviewed methods for determining whether events are independent or dependent
- Reviewed methods for calculating joint probability of multiple independent events or multiple dependent events (aka simultaneous probability)
- Reviewed similarities and differences among unconditional probability (aka marginal probability), conditional probability, and joint probability (aka simultaneous probability or intersection of events)
- Reviewed methods for calculating conditional probability of a single dependent event, including determination of dependence
- Reviewed methods for calculating conditional probability of multiple dependent events, including determination of dependence
- Reviewed methods for applying theorems of probability: complement rule, addition rule for non-mutually exclusive events (aka additive rule or union rule), conditional probability, multiplication rule (aka joint probability, simultaneous probability, or intersection of events), and law of total probability
- Reviewed applicability of (1) calculating conditional probability of a single dependent event, (2) calculating conditional probability of multiple dependent events, and (3) calculating conditional probability using Bayes’ theorem
- Reviewed methods for calculating probability based on new evidence, including determination of dependence and determination of whether to (1) use Bayes’ theorem to update an existing calculation of probability or (2) create a new calculation of probability without using Bayes’ theorem
- Reviewed similarities and differences in probability calculations between discrete and continuous random variables
- Reviewed definition, notation, terminology, components, formulas, properties, and applicability of the central limit theorem for discrete and continuous probability distributions
- Reviewed definition, notation, terminology, components, formulas, properties, and applicability of the eight most common types of discrete probability distributions
- Reviewed methods for calculating the probability for a binomial random variable, including confirming the conditions for a binomial distribution
- Reviewed definition, notation, terminology, components, PDF (probability density function), CDF (cumulative distribution function), properties, and applicability of the eight most common types of continuous probability distributions
- Reviewed methods for identifying and analyzing a continuous probability distribution with a normal distribution, including confirming the conditions for a normal distribution
- Reviewed definition, notation, terminology, components, formulas, properties, and methods for calculating a z-score for a data point in a discrete or continuous probability distribution
- Reviewed definition, notation, terminology, components, formulas, properties, and applicability of the empirical rule
- Review methods for calculating expected value for a discrete or continuous random variable
- Review methods for calculating variance for a discrete or continuous random variable
- Reviewed methods for building a risk model for a discrete random variable, including risk assessment
- Reviewed methods for building a risk model for a continuous random variable, including risk assessment
- Reviewed methods for the practical interpretation of a visualization of a discrete random variable distribution, including explanation of probability mass function (aka PMF)
- Reviewed methods for the practical interpretation of a visualization of a continuous random variable distribution, including explanation of interpretation of probability density function (aka PDF) and cumulative distribution function (aka CDF)
- Reviewed similarities and differences between the framework of normative and optimal decision theory to real-world situations, including the three different types of uncertainty (states, consequences, and actions)
- Reviewed methods for the practical application of normative decision theory to real-world situations, including the three different types of uncertainty (states, consequences, and actions)
- Reviewed methods for the practical application of optimal decision theory to real-world situations, including the three different types of uncertainty (states, consequences, and actions)
Part 1 of 10
Goal 1 Statement: Review definitions, notation, terminology, components, concepts, properties, and applicability of four main types of probability (classical, empirical, subjective, and axiomatic). NOTE: Non-probabilistic uncertainty methods (fuzzy logic, possibility theory, Dempster-Shafer theory, and info-gap decision theory) will be subsequently studied in more detail.
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review definitions, notation, terminology, and components of fundamental axioms of probability (non-negativity, normalization, and additivity)
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Goal 3 Statement: Review definitions, notation, terminology, and components of fundamental rules of probability (complement rule, addition rule for non-mutually exclusive events, conditional probability, multiplication rule, and law of total probability)
Goal 3 Plan: Read source materials
Goal 3 Work Product: None
Goal 3 Result: Completed
Goal 4 Statement: Review methods for calculating marginal probability of a single event (aka unconditional, simple, or basic probability)
Goal 4 Plan: Read source materials
Goal 4 Work Product: None
Goal 4 Result: Completed
Goal 5 Statement: Review methods for determining whether events are independent or dependent
Goal 5 Plan: Read source materials
Goal 5 Work Product: None
Goal 5 Result: Completed
Goal 6 Statement: Review methods for calculating joint probability of multiple independent events or multiple dependent events (aka simultaneous probability)
Goal 6 Plan: Read source materials
Goal 6 Work Product: None
Goal 6 Result: Completed
Goal 7 Statement: Review similarities and differences among unconditional probability (aka marginal probability), conditional probability, and joint probability (aka simultaneous probability or intersection of events)
Goal 7 Plan: Read source materials
Goal 7 Work Product: None
Goal 7 Result: Completed
Part 2 of 10
Goal 1 Statement: Review methods for calculating conditional probability of a single dependent event, including determination of dependence
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review methods for calculating conditional probability of multiple dependent events, including determination of dependence
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Part 3 of 10
Goal 1 Statement: Review methods for applying theorems of probability: complement rule, addition rule for non-mutually exclusive events (aka additive rule or union rule), conditional probability, multiplication rule (aka joint probability, simultaneous probability, or intersection of events), and law of total probability
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Part 4 of 10
Goal 1 Statement: Review applicability of (1) calculating conditional probability of a single dependent event, (2) calculating conditional probability of multiple dependent events, and (3) calculating conditional probability using Bayes’ theorem
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review methods for calculating probability based on new evidence, including determination of dependence and determination of whether to (1) use Bayes’ theorem to update an existing calculation of probability or (2) create a new calculation of probability without using Bayes’ theorem
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Part 5 of 10
Goal 1 Statement: Review similarities and differences in probability calculations between discrete and continuous random variables
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review definitions, notation, terminology, components, formulas, properties, and applicability of the central limit theorem for discrete and continuous probability distributions
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Goal 3 Statement: Review definition, notation, terminology, components, formulas, properties, and applicability of the eight most common types of discrete probability distributions
Goal 3 Plan: Read source materials
Goal 3 Work Product: None
Goal 3 Result: Completed
Goal 4 Statement: Review methods for calculating the probability for a binomial random variable, including confirming the conditions for a binomial distribution
Goal 4 Plan: Read source materials
Goal 4 Work Product: None
Goal 4 Result: Completed
Part 6 of 10
Goal 1 Statement: Review definitions, notation, terminology, components, PDF (probability density function), CDF (cumulative distribution function), properties, and applicability of the eight most common types of continuous probability distributions
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review methods for identifying and analyzing a continuous probability distribution with a normal distribution, including confirming the conditions for a normal distribution
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Goal 3 Statement: Review definition, notation, terminology, components, formulas, properties, and methods for calculating a z-score for a data point in a discrete or continuous probability distribution
Goal 3 Plan: Read source materials
Goal 3 Work Product: None
Goal 3 Result: Completed
Goal 4 Statement: Review definition, notation, terminology, components, formulas, properties, and applicability of the empirical rule
Goal 4 Plan: Read source materials
Goal 4 Work Product: None
Goal 4 Result: Completed
Part 7 of 10
Goal 1 Statement: Review methods for calculating expected value for a discrete or continuous random variable
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review methods for calculating variance for a discrete or continuous random variable
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Part 8 of 10
Goal 1 Statement: Review methods for building a risk model for a discrete random variable, including risk assessment
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review methods for building a risk model for a continuous random variable, including risk assessment
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Part 9 of 10
Goal 1 Statement: Review methods for the practical interpretation of a visualization of a discrete random variable distribution, including explanation of probability mass function (aka PMF)
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review methods for the practical interpretation of a visualization of a continuous random variable distribution, including explanation of interpretation of probability density function (aka PDF) and cumulative distribution function (aka CDF)
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Part 10 of 10
Goal 1 Statement: Review similarities and differences between the framework of normative and optimal decision theory to real-world situations, including the three different types of uncertainty (states, consequences, and actions)
Goal 1 Plan: Read source materials
Goal 1 Work Product: None
Goal 1 Result: Completed
Goal 2 Statement: Review methods for the practical application of normative decision theory to real-world situations, including the three different types of uncertainty (states, consequences, and actions)
Goal 2 Plan: Read source materials
Goal 2 Work Product: None
Goal 2 Result: Completed
Goal 3 Statement: Review methods for the practical application of optimal decision theory to real-world situations, including the three different types of uncertainty (states, consequences, and actions)
Goal 3 Plan: Read source materials
Goal 3 Work Product: None
Goal 3 Result: Completed
Insights By Scott Ernst 