Statistics and Probability

Course Title: Statistics and Probability

Course No: CSIT.216

Nature of the Course: Theory + Lab

Semester: 4

Full Marks: 60 + 20 + 20

Pass Marks: 24 + 10 + 10

Credit Hours: 3

Course Description

This course covers concept of descriptive statistics, probability, probability distributions, inferential statistics and their applications.

Course Objectives

At the end of this course the students should be able to: know basic concepts of descriptive statistics, probability and their distributions, and inferential statistics and their applications in different areas; identify existing pattern of data and their applications; apply statistical tools and techniques in rational ways; analyze the data scientifically and interpret them meaningfully.

Course Contents

1. Concepts of Statistics and Probability

2 hrs

1.1. Definition, importance, scope and limitations of statistics

1.2. Role of probability theory in statistics

1.3. Relations of statistics with information technology and e-methods

2. Concept of Population, Sample, Data and Variables and their types

3 hrs

2.1. Concept of attributes, scales, variables and their types, types of data, finite and infinite population, notation of sample, random and non-random sample

2.2. Presentation of data- organization, classification and tabulation of data, rules of tabulation (strugs rule), diagrams and graphs

2.3. Computational problems and examples

3. Measures of Descriptive Statistics

8 hrs

3.1. Measures of locations- mean, median, mode, harmonic and geometric mean, partition values, and their use and properties

3.2. Measures of dispersion- variation (absolute and relative), range, quartile deviation, mean deviation, standard deviation, coefficient of variation, Lorenz curve and gini-coefficient and their interpretations and use

3.3. Measures of skewness and kurtosis, and their use

3.4. Computational problems and examples

4. Basic Probability Theory

5 hrs

4.1. Basic terminology in probability- sample space, events, random experiment, trial, mutually exclusive events, equally likely cases, favourable events, independent and dependent events

4.2. Definition of probability- classical, statistical, subjective and axiomatic definitions, basic principles of counting, permutation and combinations

4.3. Laws of probability- additive, multiplicative, and conditional probability, Bayes theorem with examples

4.4. Random variables- discrete and continuous random variables, probability distribution of random variables

4.5. Expectation- expected value of discrete and continuous random variables, and mean and variance of random variable with illustrative examples

4.6. Computational problems and examples

5. Probability Distributions

12 hrs

5.1. Marginal and joint probability distributions, joint probability distribution of two random variables, marginal and joint probability mass functions and density functions

5.2. Mean, variance, co-variance, and correlation of random variables, independence of random variables

5.3. Discrete probability distributions- Bernoulli and binomial random variable and their distributions and moments

5.4. Computing binomial probabilities and fitting binomial distribution (relate with chi-square test of the distribution pattern of the frequency)

5.5. Poisson random variable and its distribution and moments, and computing Poisson probabilities, and also fitting of Poisson distribution (relate with chi-square test of the frequency distribution)

5.6. Continuous probability distribution- normal distribution and its moments, standardization of normally distributed random variable, measurement of areas under the normal curve

5.7. Negative exponential distribution and its moments

5.8. Present the areas of application of above probability distributions

5.9. Computational problems and examples

6. Distribution of Chi-square, t and F

2 hrs

6.1. Definitions and properties of chi-square, t and F distribution and their random variables and their distributions and their comparisons

6.2. Find the mean and variance of these distribution (Proof is not required)

6.3. Computational problems and examples

7. Inferential Statistics

8 hrs

7.1. Concept of sampling its types (probability and non probability) with merits and demerits

7.2. Steps of sample selection, determination of sample size

7.3. Sampling distributions and standard error in both case (with and without replacement)

7.4. Distinction between descriptive and inferential statistics

7.5. Concept of point and interval estimation, and criteria of good estimator

7.6. Maximum likelihood method of estimation, and estimation of mean and variance in normal distribution

7.7. Estimation of proportion in binomial distribution and confidence interval of mean in normal distribution

7.8. Concept of testing of hypothesis, level of significance, types of errors, power of the test, testing of hypothesis, concerning mean of a normal distribution in case of known variance and unknown variance

7.9. Concept of analysis of variance (ANOVA), computation of one way and two way analysis of variance

7.10. Computational problems and examples

8. Correlation and Regression

5 hrs

8.1. Simple correlation- scatter diagram, Karl Pearson's correlation coefficient, and its properties, standard error, probable error, significant test of correlation coefficient

8.2. Computation of partial and multiple correlations and their consistency (up to three variables)

8.3. Simple linear regression- model, assumptions, least square estimators, standard error, test of significance, coefficient of determination, and ANOVA (up to three variables)

8.4. Computational problems and examples

Laboratory Works

Students must perform 3 hours of practical computer lab work every week. Students will develop skills and knowledge on calculations by using real data sets manually or through computer software packages. At least one problem is to be performed for each unit. At least Excel and SPSS software should be used for data analysis.

1.Data Organization and Presentation
2.Measures of Descriptive Statistics
3.Probability Distribution Table
4.Marginal and Joint Probability Distributions
5.Binomial and Poisson Distributions and Normal Curve
6.Sampling Distributions and Interval Estimation
7.Hypothesis Testing and ANOVA
8.Correlation Analysis
9.Simple Linear Regression

Text Books

1.Sheldon M. Ross. Introduction to Probability and Statistics for Engineers and Scientists, 3rd Edition, India, Academic Press, 2005.
2.Shrestha, H.B. Statistics and Probability- Concepts and Techniques, EKTA Books Publication, Pvt. Ltd., reprint, 2008.

Reference Books

1.Richard A. Johnson, Miller and Freunds. Probability and Statistics for Engineers, 6th Edition, Indian reprint, Pearson Education, 2001.
2.Ronald E. Walole, R.H. Myers, S.L. Myers, and K. Ye. Probability and Statistics for Engineers and Scientists, 8th Edition, Indian reprint, Pearson Education, 2001.
3.Aryal, T.R. Fundamental Statistics- Concepts and Practices, Viddharthee Publication, Pvt. Ltd., 2010.
4.Martin, A. Research Methods, Statistics, IT and e-Methods. Icon Publication Pvt. Ltd, 2004.
5.Yamane, T. Mathematics for Economics. Prentice-Hall of India Pvt. Ltd, 2000.
6.Aryal, T.R. Biostatistics-For Biology, Medical and Health Sciences, Pinnacle Publication, Pvt. Ltd., 2011.
7.Harry Frank & Steven C. Althoen. Statistics Concepts and Applications. Cambridge University Press (Low price edition), 1995.
8.Murray R. Spiegel & Larry J. Stephens. Statistics (Schaum's outlines), Tata McGraw-Hill Publishing Company Ltd, New Delhi, India, 2000.
9.Kapoor J. N. and H.C. Saxena. Mathematical Statistics, S. Chand & Company Ltd., New Delhi, India, 2001.
10.Gupta S. C. and Kapoor V. K. Fundamentals of Mathematical Statistics, Sultan Chand and Sons, 2007.
11.Rohatgi V. K. and Ehsanes Saleh, A. K. MD. An Introduction to Probability and Statistics, John Wiley & Sons, 2005.
12.Hoel, Port and Stone. Introduction to Probability Theory, Houghton Mifflin Company Boston, 1971.
13.Hogg R.V and Criag, A.T. Introduction to mathematical statistics, 3rd edition, Academic Press, USA.
14.Sukubhattu, N. P. Probability Theory and Statistical Methods, 2nd edition, Asmita Publications, Kathmandu, 2063BS.
15.Miller and Fruend. Modern Elementary Statistics, Pearson Publication, 2007.
16.Shrestha, Ganga. Fundamental of Statistics. ASAN Publications, Kathmandu, Nepal, 2006.
17.Feller, W. An Introduction to Probability Theory and its Applications, Vol. 1, Third edition, John Wiley and Sons, Singapore, 2000.
18.Mayer, P. L. Introductory Probability and Statistical Applications, second edition, Oxford and IBH Publishing Co. Pvt Ltd, New Delhi, 1970.
19.Spiegel, M.R. Theory and Problems of Statistics, McGraw Hill Book Company, Singapore, 1992.

Notes:

This syllabus follows the official CSIT curriculum of Far Western University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.

Statistics I (Basic Statistics)