## Course Syllabus | BSc.CSIT

Probability and Statistics

First Semester | First Year

Tribhuvan University (TU)

**Course Title:** Probability and Statistics

**Course no:** STA-103

**Credit hours:** 3

**Full Marks:** 70+10+20 | **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 S^2 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 (Z-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, 2001.

• 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.

**Note:**

- 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.
- 5. Home works and assignments covering the lecture materials will be given

throughout the semester.