Mathematical statistics and probability are fundamental subjects in BTech CSE/IT Engineering. Probability theory provides a mathematical framework for studying the likelihood of events occurring, while statistics provides tools for analyzing and interpreting data that are subject to random variation. Students in this field learn about various probability distributions, such as the normal distribution, and statistical methods for inference, hypothesis testing, and estimation. They also learn how to apply these techniques to real-world problems in fields such as machine learning, data science, and optimization. Understanding mathematical statistics and probability is essential for CSE/IT engineers as it helps them make informed decisions and design effective algorithms for complex systems.
On this page, I am sharing Mathematical statistics & probability notes, eBook as per the syllabus of CSE/IT engineering students. These notes will help you prepare well for your engineering semester exam and score very good marks.
List of topics covered in Mathematical statistics & probability notes, eBook for BTech CSE/IT Engineering PDF File:
On this page, I am sharing Mathematical statistics & probability notes, eBook as per the syllabus of CSE/IT engineering students. These notes will help you prepare well for your engineering semester exam and score very good marks.
List of topics covered in Mathematical statistics & probability notes, eBook for BTech CSE/IT Engineering PDF File:
- UNIT -1 : Random variable and Probability distributions
- Random Variables - Single and multiple Random variables -Discrete and Continuous. Probability distribution function, mass function and density function of probability distribution. mathematical expectation and variance.
- Probability distributions: Binomial distribution – properties, mean and variance, Poisson distribution – properties, mean and variance and Normal distribution – properties, mean and variance
- UNIT -2 :Correlation and Regression: Correlation -Coefficient of correlation , Rank correlation, Regression- Regression Coefficients , Lines of Regression.
- UNIT -3 : Sampling Distributions and Statistical Inference:
- Sampling: Definitions of population ,sampling ,statistic ,parameter-Types of sampling – Expected values of sample mean and variance,Standard error- Sampling distribution of means and variance
- Parameter Estimations : likelihood estimate , interval estimate.
- Testing of hypothesis: Null and Alternative hypothesis-Type I and Type II errors, Critical region – confidence interval – Level of significance,One tailed and Two tailed test
- Large sample Tests: i) Test of significance of single mean and equality of means of two samples(cases of known and unknown variance whether equal or unequal) ii)Tests of significance difference between sample proportion and population.
- UNIT -4 : Exact Sampling Distributions(Small samples) - Exact Sampling Distributions(Small samples) Student t- distribution - properties
- i)Test of significant difference between sample and population mean
- ii)Test of difference between means of two small samples(independent and dependentsamples) F-distribution - properties –test of equality of two population variances. Chi-square distribution -properties –i)Test of goodness of fit
- iii)Test of independence of attributes
- UNIT-5 : Queuing Theory and Stochastic process -
- Queuing Theory - Structure of a queuing system its characteristics-Arrival and service process-Pure Birth and Death process Terminology of queuing system -Queuing model and its types-M/M/1 model of infinite queue (without proofs)and M/M/1 model of finite queue (without proofs).
- Stochastic Process - Introduction to stochastic process-classification and methods of description of Random process i.e,stationary and non-stationary Average values of single and two or more random process
- Markov process, Markov chain, Examples of Markov chains, Stochastic matrix.