Note: This syllabus is same for AU, CE(II Yr - II Sem), IT/CST, ME, ME(Nano Tech.), ME(Producion), Mining Engg., Mining Machinery, Mechanical Engineering (Mechatronics).

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD 
II Year B.Tech. CE - II Sem      L  T/P/D  C 
                                               4   -/-/-     4 
PROBABILITY AND STATISTICS 

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Objectives: To learn

• Understand a random variable that describe randomness or an uncertainity in certain realistic situation. It can be of either discrete or continuous type.
• In the discrete case, study of the binomial and the poisson random variables and the Normal random variable for tha continuous case predominantly describe important probability distributions. Important statistical properties for these random variables provide very good insight and are essential for industrial applications.
• Most of the random situations are described as functions of many single random variables. In this unit, the objective is to learn finctions of many random variables through joint distributions.
• The types of sampling, Sampling distribution of means, Sampling distribution of variance, Estimations of statistical parameters, Testing of hyppthesis of few unknown statistical parameters.
• The mechanism of queuing system, The characteristics of queue, The mean arrival and service rates.
• The expected queue length, The waiting line
• The random processes, The classification of random processes, Markov chain, Classification od states
• Stochastic matrix(transition probability matrix), Limiting probabilities, Applications of Markov chains

UNIT - I

Single Random variables and probability distributions: Random varaibles - Discrete and continuous. Probability distributions, mass function/ density function of probability distribution. Mathemtical Expectation, Moment about origin, Central moments Moment generating function of probability distribution. Binomial, Poisson & normal distributions and their properties. Moment generating functions of the above three distributions, and hence finding the mean and variance.

UNIT - II

Multiple Random varaibles, Correaltion & Regression: Joint probability distributions- Joint probability mass/ density function, Maginal probability mass / density functions. Covariance of two random variables, Correlation Coefficient of correlation, The rank correlation. Regression- Regression Coefficient, The lines of regression and multiple correlation & regression.

UNIT - III

Sampling Distributions and Testing of Hypothesis: Sampling: Definitions of population, sampling, statistic, parameter. Types of sampling, Expected values of Sample mean and varience, sampling distribution, Standard error, Sampling distribution of mean and sampling distribution of varience.

Parameter estmations - likelihood estimate, interval estimations.

Testing of hypothesis: Null hypothesis, Alternate hypothesis, type I, & type II errors - critical region, confidance interval, Level of significance, Once sided test, Two sided test,

Large sample tests:

1. Test of Equality of means of two samples equality of sample mean and population mean (cases of known varience & unknown varience, equal and unequal variences)
2. Tests of significance of difference between sample S.D and population S.D.
3. Tests of significance difference between sample proportion and population proportion & difference between two sample proportions.

Small sample tests: Student t-distribution, its properties; Test of significance difference between sample mean and population mean; difference between means of two small samples

Snedecor's F-distribution and it's properties. Test of equality of two population variences.

Chi-square distribution, it's properities, Chi-square test of goodness of fit

UNIT - IV

Queuing Theory: Structure of a queuing system, Operating characteristics of queuing system, Trasient and steady states, Terminology of Queuing systems, Arrival and service processes- Pure Birth-Death process Deterministic queuing models- M/M/1 Model of infinite queue, M/M/1 model of finite queue.

UNIT - V

Stochastic processes: Introduction to Stochastic Processes - Classification of Random processes, Methods of description of random processes, Stationary and non-stationary random process, Average values of single random process and two or more random processes. Markov process, Markov chain, classification of seats - Examples of Markov Chains, Stochastic Matrix.

TEXT BOOKS:

1. Higher Engineering Mathematics by Dr. B.S Grewal, Khanna Publishers
2. Probability ans Statistics for Engineers and Scientists by Sheldon M.Ross, Academic Press
3. Operations Research by S.D. Sarma,

REFERENCE BOOKS:

1. Mathematics for Engineers by K.B.Datta and M.S.Sriniva, Cengage Publications
2. Probability and Statistics by T.K.V.lyengar & B.Krishna Gandhi Et
3. Fundamentals of Mathematical Statistics by S C Gupta and V.K.Kapoor
4. Probability and Statistics for Engineers and Scientists by Jay I.Devore.

Outcomes:

• Students would be able to identify distribution in certain realistic situation. It is mainly useful for circuits as well as non-circuit branches of engineering. Also able to differentiate among many random variable involved in the probability models. It is quite useful for all branches of engineering.
• The student would be able to calculate mean and proportions (small and large sample) and to make important decisions from few samples which are taken out of unmanagably huge populations. It is Mainly useful for non-circuit branches of engineering.
• The students would be able to find the expected queue length, the ideal time, the traffic intensity and the waiting time. These are very useful tools in many engineering and data management problems in industry. It is useful for all branches of engineering.
• The student would able to understand about the random process, Markov process and Markov chains which are essentially models of many time dependent processes such as signals in communications, time series analysis, queuing systems. The student would be able to find the limiting probabilities and the probabilities in n^th state. It is quite useful for all branches of engineering.