Probability and Statistics

Course Objectives
To provide the student with a practical knowledge of the principles and concepts of probability and statistics and their application to simple engineering problems.

1. Introduction and Descriptive Statistics: (4 hours)
1.1. An overview of probability and statistics
1.2. Pictorial and tabular methods in descriptive statistics
1.3. Measures of location: mean, median, quartiles, percentiles, etc.
1.4. Measures of variability

2. Probability: (4 hours)
2.1. Sample spaces and events
2.2. Axioms, interpretations and properties of probability
2.3. Counting techniques
2.4. Conditional probability
2.5. Independence

3. Discrete Random Variables and Probability Distributions: (6 hours)
3.1. Random variables
3.2. Probability distributions for random variables
3.3. Expected values of discrete random variables
3.4. The binomial probability distribution
3.5. The hypergeometric and negative binomial distributions
3.6. The Poisson probability distribution

4. Continuous Random Variables and Probability Distributions: (6 hours)
4.1. Continuous random variables and probability density functions
4.2. Cumulative distribution functions and expected values
4.3. The Normal Distribution
4.4. The Gamma Distribution
4.5. Chi-Squared Distribution

5. Joint Probability Distributions and Random Samples: (4 hours)
5.1. Jointly distributed random variables
5.2. Expected values, covariance and correlation
5.3. Sums and averages of random variables
5.4. The central limit theorem

6. Point Estimation: (2 hours)
6.1. Some general concepts of point estimation
6.2. Methods of point estimation

7. Interval Estimation: (3 hours)
7.1. Basic properties of Confidence Interval
7.2. Large-sample Confidence interval for population Mean and Proportion
7.3. A Confidence intervals for the mean of Normal Population
7.4. Confidence interval for the Variance and Standard Deviation of a Normal Population

8. Hypothesis Testing Procedures Based on a Single Sample: (5 hours)
8.1. Hypothesis and Test Procedure
8.2. Tests about the mean of a Normal Population
8.3. Large-sample Test for population mean
8.4. Large-sample Test for a population proportion
8.5. The t-test
8.6. Some comments on selecting a test procedure

9. Hypothesis Testing Based on Two Samples: (4 hours)
9.1. z-tests for differences between two population means
9.2. The sample t-test
9.3. Analysis of paired Data
9.4. Testing for differences between population proportions

10. Simple Linear Regression and Correlation: (4 hours)
10.1. The simple linear probabilistic model and principle of least square
10.2. Correlation, Correlation coefficient and coefficient of determination
10.3. Linear and non-linear Regression
10.4. Line of Regression and coefficient of Regression

11. The Analysis of categorical Data: (3 hours)
11.1. Goodness of Fit tests when category Probabilities are completely specified
11.1.1. Goodness of fit for composite Hypothesis
11.1.2. Two way contingency Tables

Textbook:
1.0 Jay L. Devore, “Probability and Statistics for Engineering and the Sciences”, Brooks/Cole publishing Company, Monterey, California, 1982.

Reference Book:
11 Murray R. Spiegel, "Theory and Problems of Probability and Statistics", McGraw Hill, Singapore
12 D. C. Sancheti and V. K. Kapoor, "Statistics", Sultan Chand and Sons, Educational Publishers, India
13 S. C. Gupta, "Fundamental of Statistics", Himalaya Publishing House, India
14 Jeetendra P. Aryal and Arun Gautam, "Quantitative Technique Vol. II", Vidhyarthy Pustak Bhandar, Nepal
15 S. C. Gupta and V. K. Kapoor, "Fundamentals of Mathematical Statistics", Sultan Chand & Son, India