Course Language:
English
Course Objectives:
To prepare students for a career in actuarial science, graduate studies in financial
engineering/mathematics and high school teachers to teach probability and statistics
in high schools.
Course Content:
Counting. Elements of probability theory. Random variables. Conditional probability.
Bayes’ rule. Probability distributions and densities. Uniform, Bernoulli, Binomial,
Geometric, Hypergeometric, Poisson and Gaussian (normal) distributions. Uniform
density. Expectations and moments.
Course Methodology:
1: Anlatım, 2: Problem Çözme
Course Evaluation Methods:
A: Yazılı sınav, B: Ödev
Vertical Tabs
Course Learning Outcomes
|
Learning Outcomes |
Teaching Methods |
Assessment Methods |
|
1) Applies the counting principles |
1,2 |
A,B |
|
2) Computes probabilities |
1,2 |
A,B |
|
3) Knows and applies Bayes’ rule |
1,2 |
A,B |
|
4) Knows discrete probability functions |
1,2 |
A,B |
|
5) Knows continuous probability functions |
1,2 |
A,B |
|
6) Knows and applies normal distribution |
1,2 |
A,B |
Course Flow
| COURSE CONTENT | ||
| Week | Topics | Study Materials |
| 1 | Random Experiments, Sample Spaces, Events Counting Sample Points, Probability of an Event | |
| 2 | Counting Principles, Permutations and Combinations | |
| 3 | Conditional Probability and the Independence of Events. The Law of Total Probability and Bayes’ Rule | |
| 4 | Definition of Discrete Random variable. The Probability Distribution of a Discrete Random Variable. Expected value and Variance of a Random Variable | |
| 5 | The Binomial, Geometric, Negative Binomial and Hypergeometric and Poisson Probability Distributions | |
| 6 | The Poisson Probability Distribution. Moments and Moment-Generating Functions for discrete distributions. | |
| 7 | Definition of Continuous Random Variable. The Probability Distribution of a Continuous Random Variable. Expected Values for a Continuous random Variable. | |
| 8 | The Uniform, Normal and Exponential Probability Functions. | |
| 9 | The Gamma, Weibull and Beta Probability Distributions. Moments and Moment-Generating Functions for continuous distributions. | |
| 10 | Sampling Distributions Related to the Normal Distribution. The Central Limit Theorem. The Normal Approximations to the Binomial. | |
| 11 | Bivariate and Multivariate Probability Distributions. Marginal and Conditional Probability Distributions | |
| 12 | Independent Random Variables. The Covariance of Two Random Variables. The Expected Value and Variance of Linear Functions of Random Variables | |
| 13 | Finding the Probability Distribution of a Function of Random Variables. Multivariate Transformations | |
| 14 | Tchebysheff’s Inequality. Weak Law of Large Numbers. Order Statistics. | |
Recommended Sources
| RECOMMENDED SOURCES | |
| Textbook | Mathematical Statistics with Applications. Wackerly, Mendenhall, Scheaffer. Brooks/Cole |
| Additional Resources | |
Material Sharing
| MATERIAL SHARING | |
| Documents | Problem sets (Yulearn) |
| Assignments | |
| Exams | |
Assessment
| ASSESSMENT | ||
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Midterm | 1 | 100 |
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 60 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 40 | |
| Total | 100 | |
Course’s Contribution to Program
| COURSE'S CONTRIBUTION TO PROGRAM | |||||||
| No | Program Learning Outcomes | Contribution | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamental research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | x | |||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | x | |||||
| 3 | Ability form and interpret the relations between research topics in mathematics | x | |||||
| 4 | Ability to define, formulate and solve mathematical problems | x | |||||
| 5 | Consciousness of professional ethics and responsibility | x | |||||
| 6 | Ability to communicate actively | x | |||||
| 7 | Ability of self-development in fields of interest | x | |||||
| 8 | Ability to learn, choose and use necessary information technologies | x | |||||
| 9 | Lifelong education | x | |||||
ECTS
| ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION | |||
| Activities | Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 4 | 56 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 3 | 42 |
| Mid-terms (Including self study) | 1 | 14 | 28 |
| Final examination (Including self study) | 1 | 24 | 24 |
| Total Work Load | 150 | ||
| Total Work Load / 25 (h) | 6 | ||
| ECTS Credit of the Course | 6 | ||