Teaching Scheme 5 Lectures / week No. of Credits: 4 Examination Scheme CA : 30 marks
UA: 70 marks
Chapter 1) Basic tools for looking at the data (6 Lectures)
1.1. Plotting the data: Different types of plots, Line chart, Pie chart, Bar charts (stacked, grouped), Dual axis chart, bubble chart, heat map, map-based plots
1.2. Summarizing the data: Measures of Central tendency: mean, mode, median, maximum, minimum, quartiles, deciles, percentiles
1.3. Measures of dispersion: Concept of dispersion and variability of data, Measures of variability such as Range, Inter-quartile range, Variance, Standard Deviation, Coefficient of Variation.
1.4. Box plots and interpretation
1.5. Numerical/Graphical problems.
Chapter 2)Moments and shapes of distributions of data (6 Lectures)
2.1 Histogram and frequency distribution (grouped as well as ungrouped)
2.2 Symmetry of a frequency distribution, skewness, positive and negative skewness,
2.3 Measures of skewness-Pearson’s measure, Bowley’s measure, β1, γ1.
2.4 Tail behavior of a distribution, Kurtosis of a distribution, Measure of kurtosis (β2, γ2) based on higher order moments (up to 4th order), types of kurtosis: leptokurtic, platykurtic and mesokurtic.
2.5 Numerical/Graphical problems.
Chapter 3) Basic tools for looking at relationships (Bivariate data) (10 Lectures)
3.1 Bivariate data, Scatter diagram, Correlation, Positive correlation, Negative correlation, zero correlation.
3.2 Correlation and causality (basic ideas)
3.3 Karl Pearson's coefficient of correlation (r), Coefficient of determination (r2 ).
3.4 Strength of relationship for categorical variables and ranks: Kendall’s tau, Rank correlation
3.5 Regression: What is regression? Why regression? Illustrations and applications of regression and correlation.
3.6 Linear Regression
3.7 Properties of regression coefficients: bxy.byx = r 2 , byx.bxy [statement only]
3.6 Introduction to nonlinear regression models, second degree curve, growth curve models.
3.7. Numerical problems/Graphical interpretations.
Chapter 4) Basics ideas of Probability (10 Lectures)
4.1 Random Experiment, Sample Spaces (finite and countably infinite) Events: types of events, Operations on events (Basic set theory results including algebra of set operations need to be reviewed).
4.2 Probability - classical definition, probability models, axioms of probability, axiomatic definition, probability of an event, various computations of probability.
4.3 Concept and definition of: independence of two events, conditional Probability. Applications of conditional probability
4.4 Multiplication theorem, Bayes’ theorem (without proof), Concept of Posterior probability. Examples and applications
4.5 Numerical problems involving applications of above probability concepts.
Chapter 5) Categorical/count random variables and corresponding probability models (8 Lectures)
5.1 Definition of random variable, examples, discrete random variable.
5.2 Definition of probability mass function (p.m.f.), distribution function and its properties. Definition of expectation and variance. Determination of median and mode using p.m.f. Interpretation of mean, variance, mode, median etc. for a distribution
5.3 Discrete Uniform Distribution: The need, properties and applications, mean, variance [statement only]. Examples
5.4 Bernoulli random variable (categorical) , Bernoulli distribution, Properties and applications
5.5 Binomial distribution, sum of Bernoulli random variables, definition, mean, variance, additive property [statement only]. Examples and applications
5.6 Count-type random variables, Poisson distribution: definition, mean, variance, mode, additive property [statement only], Examples and applications. Ideas of equi/over- dispersion
5.7 Numerical and applied problems.
Chapter 6)Continuous random variables and some of the probability models (10 Lectures)
6.1 Definition of continuous random variable (r. v.), Probability density function (p.d.f.), Cumulative distribution function (c.d.f.), its properties. Calculation of mean, mode, median, variance, standard deviation for continuous r. v., Interpretations of these measures
6.2 Uniform distribution: p.d.f., mean, variance, nature of probability curve [statements only]. Uses and Applications
6.3 Exponential distribution: p.d.f. mean, variance, nature of probability curve, lack of memory property [statement only]. Applications and examples
6.4 Normal distribution: Motivation, p.d.f., mean, variance [statement only], nature of probability density curve, standard normal distribution, computations of probabilities using normal probability table. Uses, applications and examples
6.5 Numerical problems / Graph interpretations.
Chapter 7) Basic ideas of statistical testing of hypothesis (10 Lectures)
7.1 Concept of population and sample, random sample, SRSWR, SRSWOR, random sample from a probability distribution, parameter, estimator, statistic, standard error of estimator.
7.2 Concept of null hypothesis and alternative hypothesis, type I and type II error critical region, level of significance, one-sided and two-sided tests
7.3 Definition and interpretation of p-value.
7.4 One sample (small) testing problem (location and scale), t-tests, F-test, Assumption of normality
7.5 Two-sample (small) testing problem: t-test (paired) (Asumptions), Normality assumption
7.6 Large Sample Tests. (No derivations)
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