ALSS

Comprehensive Course

Comprehensive Probability and Statistics Course

Course Introduction

This 24-hour course covers key Probability and Statistics concepts essential for IB Mathematics (both Analysis and Applications), A-Level Mathematics, and SAT Mathematics.

Course Content

Our course is designed for those preparing for IB, A-Level, and SAT Math, aiming for perfection in their results. If you are interested in exploring and mastering advanced math concepts, this is the ideal course for you.

Course Details

Course Structure

Week 1: Introduction to Probability and Statistics (2 hours)

A. Definitions and Terminology

1. Probability: Definition, interpretation, and applications
2. Statistics: Descriptive and inferential statistics
3. Random variables: Discrete and continuous
4. Probability distributions: Probability mass function and probability density
function

B. Importance of Probability and Statistics in Mathematics

1. Decision-making and problem-solving
2. Modeling real-world phenomena
3. Interpreting and analyzing data

Week 2: Descriptive Statistics (4 hours)

A. Measures of Central Tendency

1. Mean: Definition, calculation, and properties
2. Median: Definition, calculation, and properties
3. Mode: Definition, calculation, and properties
4. Comparison and applications of central tendency measures

B. Measures of Dispersion

1. Range: Definition, calculation, and interpretation
2. Variance: Definition, calculation, and properties
3. Standard deviation: Definition, calculation, and interpretation
4. Chebyshev's inequality and its applications

C. Graphical Representations

1. Histograms: Construction and interpretation
2. Frequency polygons: Construction and interpretation
3. Box plots: Construction and interpretation
4. Comparison and applications of graphical representations

B. Measures of Dispersion

1. Range: Definition, calculation, and interpretation
2. Variance: Definition, calculation, and properties
3. Standard deviation: Definition, calculation, and interpretation
4. Chebyshev's inequality and its applications

Week 3: Probability Concepts (6 hours)

A. Basic Probability

1. Probability of an event: Definition, calculation, and properties
2. Mutually exclusive events: Definition and applications
3. Complementary events: Definition and applications

B. Conditional Probability

1. Conditional probability formula: Derivation and applications
2. Independence of events: Definition and applications

C. Combinatorics

1. Permutations: Definition, calculation, and applications
2. Combinations: Definition, calculation, and applications

D. Probability Rules

1. Addition rule: Derivation and applications
2. Multiplication rule: Derivation and applications
3. Bayes' theorem: Derivation, applications, and interpretations

Week 4: Discrete Probability Distributions (4 hours)

A. Binomial Distribution

1. Bernoulli trials: Definition and properties
2. Binomial probability formula: Derivation and applications
3. Mean and variance of a binomial distribution: Derivation and properties
4. Applications of the binomial distribution

B. Poisson Distribution

1. Poisson process: Definition and properties
2. Poisson probability formula: Derivation and applications
3. Mean and variance of a Poisson distribution: Derivation and properties
4. Applications of the Poisson distribution

Week 5: Continuous Probability Distributions (4 hours)

A. Normal Distribution

1. Standard normal distribution: Definition, properties, and standardization
2. Properties of the normal distribution: Empirical rule and applications
3. Standardizing normal random variables: Calculation and interpretation
4. Applications of the normal distribution: Probability calculations and
problem-solving

B. Other Continuous Distributions

1. Uniform distribution: Definition, properties, and applications
2. Exponential distribution: Definition, properties, and applications

Week 6: Sampling and Inference (4 hours)

A. Sampling Techniques

1. Simple random sampling: Definition, properties, and applications
2. Stratified sampling: Definition, properties, and applications
3. Systematic sampling: Definition, properties, and applications
4. Comparison and selection of appropriate sampling techniques

B. Estimation

1. Point estimation: Definition, properties, and applications
2. Interval estimation: Definition, properties, and applications
3. Confidence intervals: Calculation and interpretation

C. Hypothesis Testing

1. Null and alternative hypotheses: Definition and formulation
2. Test statistics and p-values: Calculation and interpretation
3. Type I and Type II errors: Definition, consequences, and control

Week 7: Applications and Problem-Solving (4 hours)

A. IB Mathematics Problems

Solving probability and statistics problems for IB Mathematics, A-Level
Mathematics, SAT Mathematics Test Specifications
- Exam techniques and strategies
- Common pitfalls
- Time management
- Cross-topic problems

Department Contact

Social Info

Accreditation & Certification

The Academy of Leadership Sciences Switzerland (ALSS) is an international education institution  that  offers  continuing  education,  further  education,  and  post  graduate advanced  education  courses,  workshops  and  programs  focusing  on  advanced  studies in Leadership and Management. The ALSS also offers short courses that are not credit- bearing, and do not lead to formal qualifications. All attendees who attend all the four presentations for the Introduction to Sports Law course will be awarded certificates of successful attendance by the ALSS.

Lecturer: Anastasios Karamanos, Ph.D.

Benefits

Completing a math course provides numerous benefits, including the development of critical thinking and problem-solving skills that are essential in both academic and real-world settings. It enhances logical reasoning and analytical abilities, which can be applied across various fields like science, engineering, finance, and technology. Moreover, a strong foundation in math boosts confidence in tackling complex challenges, improves decision-making, and increases career opportunities in high-demand industries. For students, it lays the groundwork for advanced studies, while for professionals, it strengthens quantitative and data interpretation skills critical for success in modern workplaces.

Professional Development

Our programs are designed to give you the edge to excel on your profession with advanced knowledge.

Quality Education

We are up-to-date with latest business trends and insights that enable us to offer qualitative education

Alumni

We have a global pool of alumni from all eh parts of the world who are excelling on their leadership journey.