JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Course Objectives:

• To introduce the concepts of Probability and Statistics.
• To learn how to apply Probability and Statistics to solve engineering and data science problems.
• To keep a balance between theory and methodology.
• To show the applications of Probability and Statistics in engineering and data science with examples.
• To learn how to apply testing of hypothesis techniques to make decisions.

Course Outcomes

At the end of the course a student acquires the ability to

• Compute probabilities using theorems in probability and probability distributions.
• Find estimates of parameters and test hypothesis about parameters.
• Establish relationship between variables using correlation and regression.
• Apply the tools in Probability and Statistics in engineering and data science.
• Take decisions by analyzing the data.

UNIT - I

Basic Statistics and Probability: Measures of Central tendency, Dispersion, Moments, Skewness and Kurtosis. Sample space and Events - Probability -The Axioms of probability - some elementary Theorems Conditional probability -Bayes’ Theorem

UNIT - II

Random variables: Discrete and continuous probability distributions. Mathematical Expectation Joint probability mass/ density function, Marginal probability mass / density function

UNIT - III

Probability Distributions and Sampling distribution: Binomial, Poisson and normal, exponential Distributions, related properties. Types of sampling, Sampling Distributions – Sampling Distribution of means ( σ known and unknown). Testing of Hypothesis I: Point Estimation - Interval Estimation –Testing of hypothesis- Null hypothesis -Alternative hypothesis- Type I and Type II errors – Critical region. Confidence interval for population mean and proportion, Test of hypotheses for one and two means - Test of hypotheses for one and two Proportions.

UNIT - IV

Testing of Hypothesis II: Student’s t-test for one and two sample means, paired t-test, confidence interval for population mean, F-test for significance of variances - Chi-Square test for one sample variance, Goodness of Fit, independence of attributes.

UNIT - V

Correlation & Regression: Scatter Plot-Coefficient of correlation- Rank Correlation-Regression - The lines of regression- Multiple regression and logistic regression

TEXT BOOKS:

• 1. S. C. Gupta and V. K. Kapoor, “Fundamentals of Mathematical Statistics”, Sultan Chand, 2014. th
• 2. Miller and Freund’s, “Probability and Statistics for Engineers”, 8 edition, PHI Page 33 of 61

REFERENCE BOOKS:

• 1. T. K. V. Iyengar & B. Krishna Gandhi, “Probability and Statistics”, S Chand, 2015. th
• 2. D. C. Montgomery and G. C. Runger, “Applied Statistics and Probability for Engineers”, 5 Edition, John Wiley, 2012. Page 34 of 61 II Year B. Tech. ITE I-Semester