This course provides students a deeper understanding about the statistical data its types, collection, interpretation, and analysis of data, learn and use the concepts of theory of probability. Moreover, this course also enables the students to learn and apply the tools for curve fitting via Linear Regression and Correlation.
Course Learning Outcomes (CLOs):
CLO:1 Illustrate basic statistics functions and identify different probability based models to predict the value of probability in various scenarios.
CLO:2 Apply probabilistic techniques to solve problems of continuous as well as discrete random variables and use curve fitting for regression problems
CLO:3 Using statistical theory, perform error analysis and predict the changes in various random systems.
1. Basic Statistics and Data Representation – Six Lectures
• Importance of statistics, population, sample, variables, and measurement
• Primary and secondary data,
• Frequency distribution, stem, and leaf display,
• Histogram, frequency polygon, cumulative frequency polygon,
• Simple & Multiple Bar diagrams
2. Measure of Central Tendency and Dispersion – Six Lectures
• Measures of central tendency, AM, GM, HM
• Quantiles, Mode, Applications of averages
• Quartile and mean deviation, Variance, Standard deviation,
• Moments, Moments ratios, Skewness, Kurtosis
• Applications of Measure of dispersion in Engineering
3. Regression, Correlation and Curve Fitting – Four Lectures
• Regression theory, Simple linear regression line
• Correlation, coefficient of correlation,
• Fitting of a first- and second-degree curves
• Principle of least squares.
4. Probability Theory – Four Lectures
• Sample Space and Set Operation
• Probability Axioms
• Events and Probabilities
• Bayes’ Theorem
5. Random Variable and Probability Distributions – Four Lectures
• Random Variables and Probability Distributions,
• Expected value and Variance.
• Binomial Random Variable and Probability Distribution,
• Poisson Random Variable and Distribution Function
6. Discrete Random Variables – Four Lectures
• Probability Mass Function
• Bernoulli, Geometric, Binomial and Poisson Random Variable
• Variance and Standard Deviation
• Conditional Probability Mass Function
7. Continuous Random Variables – Four Lectures
• Uniform distribution and Normal Distribution.
• Finding probabilities of a normally distributed random variable by using Standard Normal Curve.
• Normal Approximation to Binomial and Exponential Distribution. Curve Fitting and linear regression models.