Activity Overview
When should linear transformations be applied to the combination of random variables? Frank has steers and heifers to sell, their weights are randomly distributed. What is the probability that four randomly selected steers and two heifers will exceed the required weight? What about the required price? A program is provided for students to simulate the problem so they can compare their theoretical calculations with the simulations.
Objectives
- Concept of the sample mean as a random variable;
- Simulation of repeated random sampling;
- Linear combinations of a random variable.
Vocabulary
- Random Variable,
- Variance and standard deviation,
- Mean,
- Linear combination,
About the Lesson
The weight of Frank’s steers and heifers are normally distributed. What are the parameters if 4 steers and 2 heifers are combined? Students use a simulation to explore the distribution followed by the theoretical calculations. Students then use a simulation to explore the price per kilogram and apply linear transformations. The purpose of the activity is to illustrate an example and ‘non-example’ of linear transformations with simulations providing the supporting evidence to convince students of the corresponding theory.