EE230 PROBABILITY AND RANDOM VARIABLES
| Course Code: | 5670230 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 5.0 |
| Department: | Electrical and Electronics Engineering |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Prof.Dr. ELİF UYSAL |
| Offered Semester: | Spring Semesters. |
Course Objectives
Course Objective 1: The students will be able to understand the fundamental concepts related with probability theory.
Course Objective 2: The students will be able to understand discrete random variable concept with its extensions.
Course Objective 3: The students will be able to understand continuous random variables with its extensions.
Course Objective 4: Students will be able to interpret more advanced topics about random variables.
Course Content
Axiomatic definition of probability spaces. Combinatorial methods. Conditional probability; product spaces. Random variables; distribution and density functions; multivariate distribution; conditional distributions and densities; independent random variables. Functions of random variables; expected value, moments and characteristic functions.
Course Learning Outcomes
1.1 Construct sample space of a probabilistic experiment and interpret the axioms of probability.
1.2. Compute probabilities and conditional probabilities from an underlying experiment.
1.3 Solve problems related to Total Probability and Bayes' Theorems.
1.4. Discriminate independent events and compute their probabilities
1.5. Compute probabilities of repeated experiments by using binomial law.
2.1 Determine probability mass function (PMF) and conditional prmf of a discrete random variable (r.v.) from the underlying experiment.
2.2 Compute expected value, and variance of a discrete r.v. from its PMF.
2.3 Calculate the PMF of a discrete r.v. defined as a function of another r.v.
2.4 Obtain the joint PMF of two discrete r.v.'s. and compute marginal PMF’s from the joint PMF.
2.5. Determine independence between discrete r.v's.
3.1 Identify continuous r.v.’s through their probability density (PDF) and cumulative distribution (CDF) functions.
3.2 Compute PDF and CDF for well-known continuous distributions.
3.3 Solve problems using the conditional and joint PDF and CDF.
3.3 Calculate expectation and variance for continuous r.v.’s
4.1 Solve problems of practical interest through functions of r.v.’s.
4.2 Relate two r.v.’s based on their correlation.
4.3 Utilize transforms of r.v.s in solving particular classes of probability problems.
4.4 Use limit theorems to estimate probabilities and calculate bounds on some probabilities.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics | ✔ | |||
| 2 | An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors | ✔ | |||
| 3 | An ability to communicate effectively with a range of audiences | ✔ | |||
| 4 | An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts. | ✔ | |||
| 5 | An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives | ✔ | |||
| 6 | An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions | ✔ | |||
| 7 | An ability to acquire and apply new knowledge as needed, using appropriate learning strategies | ✔ | |||