Statistical Data Analysis Using R is a course designed to introduce students to the practical application of statistical techniques using the R programming language. The course covers essential concepts such as data import, cleaning, visualization, and descriptive statistics, followed by inferential methods including hypothesis testing, confidence intervals, correlation, regression, and analysis of variance (ANOVA). Students will also learn to handle real-world datasets, generate graphical representations, and interpret results effectively. Emphasis is placed on developing hands-on skills through coding in R, understanding outputs, and applying statistical methods to solve practical problems in various fields such as science, business, and social research. By the end of the course, learners will be proficient in using R for statistical analysis and data-driven decision making.
The theory of random variables and statistical distributions forms the foundation of probability and statistics. A random variable is a numerical outcome of a random process and can be either discrete, taking specific countable values, or continuous, taking any value within a range. Each random variable has an associated distribution that describes how its probabilities are spread across possible values. This is expressed using functions like the probability mass function (PMF) for discrete variables or the probability density function (PDF) for continuous variables. The cumulative distribution function (CDF) gives the probability that the random variable takes a value less than or equal to a specific number. Statistical distributions such as Binomial, Poisson, Normal, Exponential, and Uniform help model real-world phenomena and allow us to compute important measures like mean, variance, and standard deviation. Together, these concepts help us understand uncertainty, make predictions, and perform statistical inference.
Explain bivariate random variable, joint probability distribution
functions and their properties
Explain the concept of expectation and its properties. Explain the
concept of Moment generating functions and Characteristic function
Develop skills required to effective understanding of various
distributions.
Analyze several applications and advantages of distributions.
References
1. Gupta, S. C. and Kapoor, V. K. Fundamentals of Mathematical Statistics, Sultan Chand and Sons.
2. Gupta, S.P., Statistical Methods. Sultan Chandand Sons: NewDelhi.
3. Medhi, J. Statistical Methods, 2nd Edition, New Age International Pulbishers, 2006
4. Mukhopadhyay, P (1999) Applied Statistics, New Central Book Agency Private Limited, Kolkata.
5. Sudha G. Purohit, Sharad D. Gore and Shailaja R. Deshmukh. (2009) Statistics Using R, 2nd edition, Narosa Publishing Ho Book Agency Private Limited, Kolkata, use.
6. Tilman M. Davies. (2016) The Book of R, A First Course in R Programming and Statistics, No Starch Press
On completion of the module the student should be able to:
CO1. Demonstrate linear equations, linear independence, basis, and rank, and apply linear mappings to practical problems in various fields.
CO2. Apply concepts of analytic geometry, including norms, inner products, lengths, distances, angles, orthogonality.
CO3. Utilize various matrix decomposition techniques, including computing determinants and traces, eigenvalues and eigenvectors, Cholesky decomposition, eigen decomposition and diagonalization, and singular value decomposition.
CO4. Perform differentiation of univariate and multivariate functions, compute gradients for scalar and vector-valued functions as well as matrices, utilize useful identities for gradient computation.
CO5. Apply continuous optimization techniques, including gradient descent, constrained optimization using Lagrange multipliers, and convex optimization on real-world optimization problems efficiently and effectively.
Provide a strong foundation in matrix basics, operations, and multiplications. |
Explore vector spaces, linear independence, eigenvalues, and eigenvectors. |
Apply linear algebra concepts to real-world problems in image processing. |
Foster critical thinking and problem-solving skills in the context of linear algebra and image processing. |
Foster practical application of linear algebra principles in image processing through hands-on practicum experiences, cultivating critical thinking and problem-solving skills in real-world scenarios. |
This course will introduce mathematical techniques that form the foundation of advanced computational methods focusing on numerical methods and optimization. It enables students to comprehend and apply various problem solving strategies to address both theoretical and practical challenges in computer science.
This course helps to acquire foundational knowledge of various
types of data, Descriptive Statistics, probability theory, correlation
and regression and their real world applications. Additionally, R
programming built-in functions/Excel is used to address numerical
challenges associated with the topics discussed
This course delves into the fascinating world of human behavior within organizations. We'll explore the dynamics of individuals, groups, and the overall structure that shape how people work together.
Course Objectives:
- Gain a foundational understanding of human organizations and how individuals behave within them.
- Explore key concepts like leadership, motivation, power, conflict, and negotiation.
- Develop practical strategies to manage organizations more effectively.
By the end of this course, you will be able to:
- Analyze the behavior of individuals and groups within organizations.
- Apply frameworks and theories to understand leadership styles, motivation, and power dynamics.
- Develop strategies to improve communication, negotiation, and conflict resolution skills.
- Evaluate organizational culture and contribute to positive change initiatives.
- Become a more informed and effective member of any organization.
This course will equip you with the knowledge and skills to navigate the complexities of human behavior in organizations. Through lectures, discussions, case studies, and practical exercises, you'll gain valuable insights applicable to any work environment.
This course is designed to introduce students to the fundamentals of R and Python, two of the most powerful programming languages used in data science, statistics, and analytics. The course is entirely practical and will be conducted using Google Colab, a cloud-based platform that allows students to write and execute code interactively without needing to install any software.
This course contains representative works to acquaint the student with the representative works of modern European drama and the social and cultural contexts that inform modern European Drama.