Course no: STA-103 Full Marks: 70+10+20
Credit hours: 3 Pass Marks: 28+4+8
Nature of course: Theory (3 Hrs.) + Lab (3 Hrs.)
Course Synopsis: Concept of descriptive statistics, probability, probability
distributions, inferential statistics and their applications.
Goal: This course enhances the ability of students in computing and understanding summary statistics; understanding the concept of probability and probability distributions with their applications in statistics. Finally, students will develop their ability of using inferential statistics in decision-making processes.
Course Contents:
Unit 1. Introduction 2 Hrs.
Scopes and limitations of statistics in empirical research; Role of probability theory in
statistics; Role of computer technology in statistics
Unit 2. Descriptive Statistics 6 Hrs.
Measures of location: mean, median, mode, partition values and their properties;
Measures of dispersion: absolute and relative measure of variation; range, quartile deviation, standard deviation; Other measures: Coefficient of variation; Measures of skewness and kurtosis.
Unit 3. Probability 5 Hrs.
Introduction of probability: Basic terminology in probability: sample space, events, random experiment, trial, mutually exclusive events, equally likely events, independent events; Definitions of probability: Classical, statistical, axiomatic definitions; Basic principles of counting; Laws of probability: Additive and multiplicative; Conditional probability; Bayes' Theorem.
Unit 4. Random Variable and Expectation 2 Hrs.
Random Variables: Discrete and continuous random Variables; Probability
distribution of random variables; Expected value of discrete & continuous random Variable.
Unit 5. Jointly Distributed Random Variables and Probability Distributions 4 Hrs.
Joint Probability Distribution of two random variables: Joint probability mass
functions and density functions; Marginal probability mass and density functions; Mean, variance, covariance and correlation of random variables; Independent random variables; Illustrative numerical problems.
Unit 6. Discrete Probability Distributions 5 Hrs.
Bernoulli and binomial random variable and their distributions and moments;
Computing binomial probabilities; Fitting of binomial distribution; Poisson random variable and its distribution and moments; Computing Poisson probabilities; Fitting of Poisson distribution.
Unit 7. Continuous Probability Distributions 6 Hrs.
Normal distribution and its moments; Standardization of normally distributed random variable; Measurement of areas under the normal curve; Negative exponential distribution and its moments; Concept of hazard rate function.
Unit 8. Chi-square, t and F Distribution 4 Hrs.
Characteristics function of normal random variable; Distribution of sum and mean of n independent normal random variables; Canonical definitions of chi-square, t and F random variables and their distributions; Joint distribution of X and S2 in case of normal distribution.
Unit 9. Inferential Statistics 7 Hrs.
Simple random sampling method and random sample; Sampling distribution and
standard error; Distinction between descriptive and inferential statistics; General concept of point and interval estimation; Criteria for good estimator; Maximum likelihood method of estimation; Estimation of mean and variance in normal distribution; Estimation of proportion in binomial distribution; Confidential interval of mean in normal distribution; Concept of hypothesis testing; Level of significance and power of a test; Tests concerning the mean of a normal distribution case – when variance is known (-test) and unknown (t-test)
Unit 10. Correlation and Linear Regression 4 Hrs.
Simple Correlation: Scatter diagram; Karl Pearson's correlation coefficient and its properties, Simple Linear Regression: Model and assumptions of simple linear regression; Least square estimators of regression coefficients; Tests of significance of regression coefficients; Coefficient of determination
Text Books: Sheldon M. Ross, Introduction to Probability and Statistics for
Engineers and Scientists, 3rd Edition, India: Academic Press, 2005.
References:
- Richard A. Johnson, Miller and Freund's probability and Statistics for Engineers, 6th Edition, Indian reprint: Pearson Education,
- Ronald E. Walpole, R.H. Myers, S.L. Myers, and K. Ye, Probability
and Statistics for Engineers and Scientists, 7th Edition, Indian
reprint: Pearson Education, 2005.
- Theory and practice should go side by side.
- It is recommended 45 hours for lectures and 15 additional hours for tutorial class for completion of the course in the semester.
- SPSS software should be used for data analysis.
- Students should have intermediate knowledge of Mathematics.
- Home works and assignments covering the lecture materials will be given
throughout the semester.
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