Unit 6: Random Variables and Probability Distributions

The distribution of measures for individuals within a sample or population describes variation. The value of a statistic varies from sample to sample. How can we determine whether differences between measures represent random variation or meaningful distinctions?

Statistical methods based on probabilistic reasoning provide the basis for shared understandings about variation and about the likelihood that variation between and among measures, samples, and populations is random or meaningful.

Statistical tools allow us to represent and describe patterns in data and to classify departures from patterns. Simulation and probabilistic reasoning allow us to anticipate patterns in data and to determine the likelihood of errors in inference.

Distinguish between discrete and continuous random variables.

Transform and combine random variables.

Understand binomial and geometric random variables.

Students will demonstrate mastery by solving complex word problems where they must first adjust a variable by a constant and then combine it with another variable, such as calculating the total profit of a business after accounting for fixed costs and variable sales. They will provide written interpretations of the expected value in the context of games of chance or insurance policies. They will also show they can correctly identify when it is inappropriate to combine variations because the two variables are not independent. Finally, they will use their findings to make predictions about the likelihood of specific outcomes occurring in the long run.