## MAT 212: Probability and Statistics for Science & Engineering

### Course rationale

The knowledge of statistics is imperative to understand and analyze physical phenomenon. The real-life problems are becoming more complicated as more and more information are being added every day, so the application of physical laws is also becoming difficult with this. With appropriate statistical methods students will be able to analyze complex and large number of data and will be able to make decisions and draw valid conclusions.

### Course content

Review of Mathematics: Factorial, Permutation and Combination. Probability: Random experiment, Sample space, different types of events. Rules of Probability: Addition rule, Complement rule, Conditional rule, Multiplication rule and Bayes’ rule. Random Variable: Discrete and Continuous random variables, Probability mass functions, Probability density functions, Cumulative distribution functions, Cumulative density function, Expectation, Variance and Moment generating function. Discrete Probability Distributions: Binomial, Poisson, Geometric, Uniform, Negative binomial and Hypergeometric distributions. Continuous Probability Distributions: Continuous uniform distributions, Exponential distributions, Normal distributions. Descriptive Statistics: Measures of central tendencies, Measures of variation, Frequency analysis, graphical analysis. Inference: Confidence intervals for Population mean and Population variance. Regression analysis: Correlation analysis between two variables, Simple linear regression and prediction.

### Course objectives

- Identify the correct counting technique and count the possible outcomes from an experiment.
- Application of appropriate probability rules and calculate the chance of the outcomes of an experiment.
- Calculation of probability functions of discrete and continuous random variables, expectations and standard deviations and interpret the findings.
- Identify and apply suitable probability distributions and calculate their expectations and standard deviations.
- Introduction to descriptive statistics, graphs and interpretation of the findings.
- Construction of Confidence intervals for population mean and population standard deviation to find the best estimate of the parameters.
- Use Correlation and regression theory to identify the relationship between two variables and hence forecast the dependent variable.

### References

- Montgomery, D.C.and Runger G.C.(2011), AppliedStatistics and Probabilityfor Engineers (5th edition), John Wiley & Sons, Inc.
- Murray r. spigel and larry j. stephens (2008), schaum’s outline of theory and problems of statistics (fourth edition), schaum’s outline series, mcgraw-hill.
- Ronald e. walpole, raymond h. myers and sharon l. myers, probability & statistics for engineers & scientists (ninth edition)