- Introduction to Statistics. Definition of terms and concepts with simple illustrations. Measures of central tendency: Mean, mode, medium. Measures of dispersion: Variance, standard deviation, range. Organizing random data. Introduction to Excel statistics tools.
- Basic Probability. Probability based on: equally likely events, frequency, axioms.
Permutations and combinations of distinct objects. Total, joint, conditional probabilities. Examples related to systems engineering.
- Discrete Random Variables. Bernoulli trial. Binomial distributions. Poisson distribution. Discrete probability density functions and cumulative distribution functions. Excel examples.
- Continuous random variables. Normal distribution. Uniform distribution. Triangular distribution. Log-normal distributions. Discrete probability density functions and cumulative distribution functions. Excel examples.
- Sampling Distributions. Sample size considerations. Central limit theorem.
- Functions of Random Variables. (Propagation of errors) Sums and products of random variables. Tolerance of mechanical components. Electrical system gains.
- System Reliability. Failure and reliability statistics. Mean time to failure. Exponential distribution. Gamma distribution. Weibull distribution.
- Confidence Level. Confidence intervals. Significance of data. Margin of error. Sample size considerations. P-values.
- Hypotheses Testing. Error analysis. Decision and detection theory. Operating characteristic curves. Inferences of two-samples testing, e.g. assessment of before and after treatments.
- Probability Plots and Parameter Estimation. Percentiles of data. Box whisker plots.
Probability plot characteristics. Excel examples of Normal, Exponential and Weibull plots.
- Regression Analysis. Introduction to linear regression, Error variance, Pearson linear correlation coefficient. Residuals pattern. Excel examples.
- Other Topics of Interest to Class.