### Probability and Statistics

Course No.: STA-103

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.

__Goals__: 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.

Download PDFSyllabus Of "Probability and Statistics"

**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, 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:

1. Theory and practice should go side by side.

2. It is recommended 45 hours for lectures and 15 additional hours for tutorial class for completion of the course in the semester.

3. SPSS software should be used for data analysis.

4. Students should have intermediate knowledge of Mathematics.

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

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