COURSE INFORMATION Course Title: STATISTICAL TECHNIQUES IN HYDROLOGY

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
CE 452	B	1	2	2	0	3	7.5

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Mirjam Ndini
Second Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Classroom and Meeting Time:
Course Description:	Introduction to probability and statistics applications in hydrology: random variables and their statistical properties, commonly used probability distributions in hydrology. Statistical analysis of hydrologic data: frequency analysis, hypothesis testing, analysis of variance. Hydrologic time series analysis and forecasting.
Course Objectives:	This course emphasizes engineering applications of hydrologic science. Concept of probability and statistics is very important to solve various civil engineering problems. In this course, basic probability concept and different probabilistic models will be discussed for the vital role of such methods in civil engineering. Concept and definition of random variables and different functions will be covered in the initial part of the course. Both univariate and multivariate functions will be discussed. The concept of joint, marginal and conditional probability distributions, moments, expectations, the correlation will also be discussed. Afterward, the focus is given to commonly used probability distribution functions in civil engineering. Both discrete (binomial distribution, poisson’s distribution) and continuous distribution functions (normal, lognormal, exponential distribution, gamma distribution) will be discussed.

COURSE OUTLINE

Week	Topics
1	Introduction: Role of Probability in Civil Engineering Problems; Examples.
2	Random Events: Definition of basic random events; Application of set theory in definition of composite event operations;
3	Probability of events and definition of probability axioms; Solution of real life examples from civil engineering.
4	Random Variables: Definition of random variables - discrete and continuous;Probability definitions - PMF, 6 NPTEL http://nptel.iitm.ac.in Civil Engineering Pre-requisites: Basic knowledge of Mathematics. Coordinators: Dr. Rajib Maity Department of Civil EngineeringIIT Kharagpur PDF, CDF;
5	Moments and expectations.
6	Functions of Random Variables: Definition of probability distributions of functions of single random variables - exact methods and approximate methods;
7	Moments and expectations of functions - direct and indirect methods.
8	Multiple Random Variables: Definition of joint, marginal, and conditional probability distributions; Definitions of moments and expectations, including the definition of correlation coefficient;
9	Functions of multiple random variables.
10	Common Probability Models: Discrete random variables - binomial distribution, Poisson’s distribution; Continuous random variables - exponential distribution, gamma distribution;
11	Central limit theorem; Normal and lognormal distributions;
12	Extremal distributions.
13	Statistics and sampling: Goodness of fit tests; regression and correlation analyses; estimation of distribution parameters from statistics; Hypothesis testing and significance;
14	Bayesian updating of distributions.

Prerequisite(s):	MTH 205 Probability and Statistics for Engineers CE 240 Engineering Hydrology
Textbook:	1. Papoulis, A, and S. U. Pillai (2002), Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York. 2. Richard A. Jonson and C. B. Gupta (2005), Miller and Freund’s Probability and Statistics for Engineers, Pearson Education, Inc., United States. 3. West M. and J. Harrison (1997), Bayesian Forecasting and Dynamic Models, Springer-Verlag, New York.
Other References:
Laboratory Work:
Computer Usage:	yes. applications
Others:	No

COURSE LEARNING OUTCOMES

1	The student will be introduce to the field of statistics and how engineers use statistical methodology as part of the engineering problem-solving process.
2	The student will introduces to some engineering applications of statistics, including building empirical models, designing engineering experiments, and monitoring manufacturing processes.
3	The course will cover the basic concepts of probability, discrete and continuous random variables, probability distributions, expected values, joint probability distributions, and independence.
4	The student will learn statistical methods with random sampling; data summary and description techniques, histograms, box plots, and probability plotting; and several types of time series plots.
5	The student will learn some of the important properties of estimators, the method of maximum likelihood, the method of moments, and Bayesian estimation.
6	They will be introduced to the confidence intervals for means, variances or standard deviations, proportions, prediction intervals, and tolerance intervals.
7	Presents tests and confidence intervals for two samples. There are detailed information and examples of methods for determining appropriate sample sizes. We want the student to become familiar with how these techniques are used to solve real-world engineering problems and to get some understanding of the concepts behind them. We give a logical, heuristic development of the procedures.

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
MSc in Civil Engineering, Profile: Construction Materials Engineering Program
1	an ability to apply knowledge of mathematics, science, and engineering	3
2	an ability to design a system, component, or process to meet desired needs	3
3	an ability to function on multidisciplinary teams	3
4	an ability to identify, formulate, and solve engineering problems	3
5	an understanding of professional and ethical responsibility	3
6	an ability to communicate effectively	3
7	the broad education necessary to understand the impact of engineering solutions in a global and societal context	3
8	a recognition of the need for, and an ability to engage in life long learning	3
9	a knowledge of contemporary issues	3
10	an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice	3
11	skills in project management and recognition of international standards and methodologies	3

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Homework	2	5
Presentation	2	5
Case Study	1	10
Term Paper	1	30
Final Exam	1	40
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	3	48
Hours for off-the-classroom study (Pre-study, practice)	16	3	48
Mid-terms			0
Assignments	2	2.5	5
Final examination	1	2.5	2.5
Other	4	21	84
Total Work Load:			187.5
Total Work Load/25(h):			7.5
ECTS Credit of the Course:			7.5