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Probability and Statistics
Engineering & Social Sciences Program
Madrid, Spain
Dates: 1/16/25 - 6/4/25
Probability and Statistics
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Physics
Instruction in: English
Course Code: 18301
Transcript Source: Partner Institution
Course Details: Level 100
Recommended Semester Credits: 3
Contact Hours: 42
DESCRIPTION
1. Introduction to statistics
1.1. General concepts
1.2. Sampling methods
1.3. Introduction to visualization tools
2. Probability space
2.1. Basic properties
2.2. Independence and conditional probability
2.3. Total probability
2.4. Bayes theorem
3. Univariate statistics
3.1. Visualization techniques
3.2. Characteristic measures
3.3. Transformations
4. Random variables
4.1. Distributions
4.2. Characteristic measures
4.3. Transformations
4.4. Examples
5. Introduction to statistical inference
5.1. Population and sample
5.2. Sampling distribution of a statistic
5.3. The sample mean distribution
5.4. Estimation and estimators
5.5. Method of moments
5.6. Maximum likelihood
6. Confidence intervals
6.1. For the mean
6.2. For the proportion
6.3. For the variance
7. Hypothesis testing
7.1. Introduction to hypothesis testing
7.2. Type I and Type II errors
7.3. Power of a Statistical Test
7.4. p-value
8. Nonparametric goodness-of-fit tests
8.1. Chi-square tests
8.2. Kolmogorov-Smirnov tests
1.1. General concepts
1.2. Sampling methods
1.3. Introduction to visualization tools
2. Probability space
2.1. Basic properties
2.2. Independence and conditional probability
2.3. Total probability
2.4. Bayes theorem
3. Univariate statistics
3.1. Visualization techniques
3.2. Characteristic measures
3.3. Transformations
4. Random variables
4.1. Distributions
4.2. Characteristic measures
4.3. Transformations
4.4. Examples
5. Introduction to statistical inference
5.1. Population and sample
5.2. Sampling distribution of a statistic
5.3. The sample mean distribution
5.4. Estimation and estimators
5.5. Method of moments
5.6. Maximum likelihood
6. Confidence intervals
6.1. For the mean
6.2. For the proportion
6.3. For the variance
7. Hypothesis testing
7.1. Introduction to hypothesis testing
7.2. Type I and Type II errors
7.3. Power of a Statistical Test
7.4. p-value
8. Nonparametric goodness-of-fit tests
8.1. Chi-square tests
8.2. Kolmogorov-Smirnov tests