Probability and Statistics for Engineering (IME 3140, IME 3011)

Objectives:

1. Understand and describe sample spaces and events for random experiments with graphs and diagrams.
2. Interpret probabilities and use probabilities of outcomes to calculate probabilities of events in discrete sample spaces.
3. Calculate the probabilities of joint events such as unions and intersections from the probabilities of individual events.
4. Calculate conditional probability

Part 1: Key Definitions and Terms

Objectives:

1. Determine probabilities from probability mass functions and the reverse.
2. Determine probabilities from cumulative distribution functions.
3. Determine means and variances for discrete random variables.
4. Select an appropriate discrete probability distribution to calculate probabilities in specific applications.
5. Calculate probabilities, and calculate means and variances, for each of the probability distributions presented.

Part 1: A Generic Discrete Distribution

Part 2: Uniform and Binomial Distributions

Objectives:

1. Determine probabilities from probability density functions.
2. Determine probabilities from cumulative distribution functions.
3. Determine means and variances for continuous random variables.
4. Select an appropriate continuous probability distribution to calculate probabilities in specific applications.
5. Calculate probabilities, and calculate means and variances, for each of the probability distributions presented.

Part 1: A Generic Continuous Distribution

Part 2: Continuous Uniform Distribution

Objectives:

1. Define the Poisson Process and its significance in probability and statistics.
2. Identify real-world scenarios where the Poisson Process is an appropriate model (e.g., call arrivals at a call center)
3. Derive the probability distribution function for the number of events in a given interval.
4. Understand and apply the relationship between the exponential distribution and the Poisson Process.
5. Solve problems using the Poisson Process to calculate probabilities in different scenarios.

Part 1: Poisson and Exponential Random Variables

Part 2: Erlang Random Variable

Objectives:

1. Differentiate between covariance and correlation, highlighting their unique characteristics.
2. Describe how covariance measures the relationship between two variables.
3. Interpret the sign and magnitude of covariance values.
4. Calculate covariance and correlation for a given data set.
5. Critically evaluate the use of covariance and correlation in statistical analysis, recognizing potential pitfalls and misinterpretations.

Part 1: Poisson and Exponential Random Variables

Objectives:

1. Identify the role that statistics can play in the engineering problem-solving process.
2. Discuss how variability affects the data collected and used for engineering decisions.
3. Discuss the different methods that engineers use to collect data.
4. Compute and interpret the sample mean, sample variance, sample standard deviation, sample median, and sample range.
5. Explain the concepts of sample mean, sample variance, population mean, and population variance.
6. Construct and interpret visual data displays, including the histogram, and the box plot.
7. Explain the concept of random sampling.
8. Explain how to use box plots, and other data displays, to visually compare two or more samples of data.
9. Know how to use simple time series plots to visually display the important features of time-oriented data.

Part 1: Data Analysis Fundamentals

Part 2: Minitab Demonstrations

Objectives:

1. Structure engineering decision-making as hypothesis tests.
2. Test hypotheses on the mean of a normal distribution using either a Z-test or a t-test procedure.
3. Use the P-value approach for making decisions in hypothesis tests.
4. Compute power & Type II error probability.  Make sample size selection decisions for tests on means, variances & proportions.
5. Explain & use the relationship between confidence intervals & hypothesis tests.

Part 1: Sampling Distribution

Part 2: Hypothesis Testing Formulation & Procedure

Objectives:

1. Construct confidence intervals for engineering decision-making.
2. Utilize confidence intervals for making decisions in hypothesis tests.
3. Test hypotheses on the mean of a normal distribution using a t-test procedure.
4. Use the P-value approach and confidence intervals for making decisions in t-tests.
5. Conduct hypothesis tests on the proportion of a population using multiple methods.

Part 1: Confidence Interval

Part 2: T-test

Objectives:

1. determine when to use a two-sample t-test and a paired t-test
2. perform hypothesis tests on two population means (standard deviations known versus standard deviations unknown) using critical regions, P-values, and confidence intervals
3. perform paired t-tests on two population means using critical regions, P-values, and confidence intervals