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Advanced Probability and Statistical Methods

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Advanced Probability and Statistical Methods

Dieser Kurs ist Teil von Spezialisierung „Statistical Methods for Computer Science“

Dozenten: Ian McCulloh

Bei enthalten

Mehr erfahren

6 Module

Verschaffen Sie sich einen Einblick in ein Thema und lernen Sie die Grundlagen.

Stufe Mittel

Empfohlene Erfahrung

5 Wochen zu vervollständigen

unter 10 Stunden pro Woche

Flexibler Zeitplan

In Ihrem eigenen Lerntempo lernen

6 Module

Verschaffen Sie sich einen Einblick in ein Thema und lernen Sie die Grundlagen.

Stufe Mittel

Empfohlene Erfahrung

5 Wochen zu vervollständigen

unter 10 Stunden pro Woche

Flexibler Zeitplan

In Ihrem eigenen Lerntempo lernen

Was Sie lernen werden

Learn to analyze relationships between random variables through joint probability distributions and independence concepts.
Understand how to calculate and interpret expected values, variances, and correlations for random variables.
Acquire essential skills in conducting statistical tests, including T-tests and confidence intervals, for data analysis.
Explore the principles of Markov chains and their applications in modeling systems with memoryless properties and calculating entropy.

Kompetenzen, die Sie erwerben

Kategorie: Probability Distribution
Kategorie: Statistical Analysis
Kategorie: Statistical Hypothesis Testing
Kategorie: Statistical Modeling
Kategorie: Data Analysis
Kategorie: Statistical Programming
Kategorie: Markov Model
Kategorie: Statistical Methods
Kategorie: Probability & Statistics
Kategorie: Data Science
Kategorie: Correlation Analysis
Kategorie: Statistical Inference
Kategorie: Probability
Kategorie: Regression Analysis

Werkzeuge, die Sie lernen werden

Kategorie: Statistical Software
Kategorie: R Programming

Wichtige Details

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22 Aufgaben

Unterrichtet in Englisch

91%

of learners achieved a positive career outcome

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Dieser Kurs ist Teil der Spezialisierung Spezialisierung „Statistical Methods for Computer Science“

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In diesem Kurs gibt es 6 Module

The course "Advanced Probability and Statistical Methods" provides a deep dive into advanced probability and statistical methods, essential for mastering data analysis in computer science. Covering joint distributions, expectation, statistical testing, and Markov chains, you'll explore key concepts and techniques that underpin modern data-driven decision-making. By engaging with real-world problems, you’ll learn to apply these methods effectively, gaining insights into the relationships between random variables and their applications in diverse fields.

Completing this course equips you with the skills to analyze complex data sets and make informed predictions, enhancing your proficiency in statistical reasoning and inference. Unique to this course is its blend of theoretical foundations and practical applications, ensuring that you can not only understand the principles but also implement them using tools like R. Whether you're pursuing a career in data science, machine learning, or any data-centric discipline, this course will empower you to tackle challenging statistical problems and drive meaningful insights from data.

Moduldetails

This course provides a comprehensive overview of probability theory and statistical inference, covering joint probability distributions, independence, and conditional distributions. Students will explore expected values, variances, and key statistical theorems, including the central limit theorem. Hypothesis testing, regression analysis, and stochastic processes such as Poisson processes and Markov chains will also be examined. Through practical applications and problem-solving, participants will gain essential skills in data analysis and interpretation.

Das ist alles enthalten

2 Lektüren1 Plug-in

This module presents the joint distributions of multiple random variables, both discrete and continuous and introduces the concept of independence.

Das ist alles enthalten

9 Videos4 Lektüren5 Aufgaben1 Unbewertetes Labor

9 VideosInsgesamt 126 Minuten

Overview14 Minuten
Joint Distributions15 Minuten
Joint Probability Space and Joint PMF24 Minuten
Joint Density Function (PDF)14 Minuten
Expected Value and Marginal Distributions6 Minuten
Joint PDF Example Problem12 Minuten
Conditional Joint Probability Distributions13 Minuten
Independence of Joint Random Variables15 Minuten
R Tutorial15 Minuten

4 LektürenInsgesamt 480 Minuten

Reading References120 Minuten
Reading References120 Minuten
Reading References120 Minuten
Reading References120 Minuten

5 AufgabenInsgesamt 120 Minuten

Joint Distributed Random Variables15 Minuten
Advanced Concepts in Joint Density Functions and Marginal Distributions15 Minuten
Exploring Joint PDFs and Conditional Probability Distributions15 Minuten
Independence of Joint Random Variables and R Implementation15 Minuten
Joint Distributed Random Variables60 Minuten

1 Unbewertetes LaborInsgesamt 60 Minuten

Practice Lab: Exploring Joint PMFs, Density Functions, and Probability Distributions with R60 Minuten

This module focuses on the expectation of a random variable and joint random variable. Students will solve problems using the linearity of expectation and identify when its application is inappropriate. We will also explore variance, covariance, and correlation.

Das ist alles enthalten

7 Videos3 Lektüren4 Aufgaben1 Unbewertetes Labor

7 VideosInsgesamt 65 Minuten

Expected Value & Median7 Minuten
Mean Time to Failure9 Minuten
Linearity of Expectation9 Minuten
Hat Check Problem7 Minuten
Sum of Indicator Variables7 Minuten
Variance16 Minuten
R Tutorial10 Minuten

3 LektürenInsgesamt 540 Minuten

Reading References180 Minuten
Reading References180 Minuten
Reading References180 Minuten

4 AufgabenInsgesamt 105 Minuten

Understanding Expected Value, Median, and Mean Time to Failure15 Minuten
Linearity of Expectation and the Hat Check Problem15 Minuten
Variance Analysis and Indicator Variables with R Tutorial15 Minuten
Expectation60 Minuten

1 Unbewertetes LaborInsgesamt 60 Minuten

Practice Lab: Exploring Expectations and Ambulance Travel Distance Using R60 Minuten

This module will apply several limit theorems to solve problems to include the central limit theorem, the Markov inequality, and the Chebyshev inequality. We will also prove Murphy’s Law.

Das ist alles enthalten

9 Videos4 Lektüren5 Aufgaben1 Unbewertetes Labor

9 VideosInsgesamt 94 Minuten

Rare Events & Markov8 Minuten
Markov Examples13 Minuten
Murphy's Law7 Minuten
Chebyshev Inequality6 Minuten
Central Limit Theorem10 Minuten
Example CLT9 Minuten
Hypothesis Test15 Minuten
Card Trick12 Minuten
R Tutorial 14 Minuten

4 LektürenInsgesamt 240 Minuten

Reading References60 Minuten
Reading References60 Minuten
Reading References60 Minuten
Reading References60 Minuten

5 AufgabenInsgesamt 120 Minuten

Markov Chains, Rare Events, and Murphy's Law15 Minuten
Chebyshev Inequality and the Central Limit Theorem15 Minuten
Central Limit Theorem Examples and Hypothesis Testing15 Minuten
Card Tricks and R Tutorial for Statistical Analysis15 Minuten
Inequalities and Central Limit Theorem60 Minuten

1 Unbewertetes LaborInsgesamt 60 Minuten

Practice Lab: Statistical Distributions and Hypothesis Testing in R60 Minuten

This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.

Das ist alles enthalten

4 Videos2 Lektüren3 Aufgaben1 Unbewertetes Labor

4 VideosInsgesamt 98 Minuten

Statistical Hypothesis Testing10 Minuten
T-Test20 Minuten
Regression37 Minuten
R Tutorial- Statistical Testing31 Minuten

2 LektürenInsgesamt 120 Minuten

Understanding Data and Basis Statistics60 Minuten
Understanding Data and Basis Statistics60 Minuten

3 AufgabenInsgesamt 90 Minuten

Statistical Hypothesis Testing and T-Tests15 Minuten
Regression and R Tutorial15 Minuten
Statistical Testing60 Minuten

1 Unbewertetes LaborInsgesamt 60 Minuten

Practice Lab: Simulation of Arbitrary Random Variables and Statistical Analysis in Medical Imaging60 Minuten

This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.

Das ist alles enthalten

8 Videos4 Lektüren5 Aufgaben1 Unbewertetes Labor

8 VideosInsgesamt 103 Minuten

The Poisson Process13 Minuten
Examples of the Poisson Process18 Minuten
Markov Chains7 Minuten
Markov Chain Example21 Minuten
Limiting Probabilities8 Minuten
R Tutorial14 Minuten
Markov chain using Jupyter Notebook9 Minuten
Applying Markov Chain14 Minuten

4 LektürenInsgesamt 135 Minuten

Reading References40 Minuten
Reading References40 Minuten
Reading References40 Minuten
Application of Markov Chains to COVID-19 estimation COVID Bayesian Data August PDF15 Minuten

5 AufgabenInsgesamt 120 Minuten

Statistical Hypothesis Testing and T-Tests15 Minuten
Regression and R Tutorial15 Minuten
Limiting Probabilities and R Tutorial15 Minuten
Mastering Markov Chains: From Jupyter Notebook Basics to Real-World Applications15 Minuten
Markov Chain60 Minuten