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
- Duration of the Course: 8 weeks (every Thursday, Monday one hour and thirty minutes per class at 18h00 CET)
- Language English
- Start Date 09 January 2025
- Study Options 100 % online per Zoom
- Tutorial fees for the whole course CHF 660 to be paid at least one week before the course starts.
- We welcome students who are passionate about achieving excellence in Mathematics. Our course is designed for those preparing for IB, A-Level, and SAT Math.
- Internet access and an email address are required.
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
Academics List
Related Downloads
Department Contact
- Hotline +41 (0)44 308 35 22
- World Trade Center Leutschenbachstrasse 95 CH-8050 Zürich
- info@alss-edu.ch
- Mon - Fri : 09:00 - 18:00
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.
-
An experienced educator with over 20 years of teaching Mathematics, Physics, Statistics, and Business Management, specializing in IB, A-level, and SAT exam preparation.
Holding an MSc in Mechanical Engineering (Distinction) from Imperial College London and a PhD in Business Management from the University of Cambridge.
Dedicated to delivering engaging, personalized lessons that inspire intellectual curiosity and build confidence.
Lessons follow a collaborative, step-by-step approach, empowering students to master their subjects and excel in exams.
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.