Education Technology

# Statistics: Geometric Distributions

by Texas Instruments

#### Overview

Students simulate a geometric distribution of rolling a die to determine experimental probabilities and calculate theoretical probabilities.

#### Key Steps

• Problem 1 introduces students to the geometric distribution. They to determine whether several given situations represent a geometric distribution.

In the second problem, students will investigate the probability of the first 5 appearing on the fourth roll. Students will use the Random Integer command to simulate the geometric distribution.

• They will combine their results with other classmates and calculate the experimental probability. Students will use a histogram to help calculate probabilities and form conclusions.

• In Problem 3, students will explore the theoretical probabilities of a geometric distribution using the Geometric Pdf command. They will then derive the formula for calculating the probability of the first 5 appearing on the nth roll. Then students will graph the probabilities as a scatter plot and determine the regression equation. They will algebraically verify that the formula and the regression equation are the same.