SOCR EduMaterials Activities CoinSampleExperiment

Coin Sample Experiment

• Description:

The coin sample experiment is a simple demonstration of the Bernoulli trial. It consists of n coins being tossed with the probability p of heads as an outcome. Random variable Ij gives the outcome for coin j with 1 representing heads and 0 representing tails. Each trial will be recorded and updated in the data table. Parameters n and p can be modified with scroll bars.

• Goals:

To provide a simple method for natural occurring phenomena that have two distinct categorical outcomes (e.g. yes/no, true/false, success/failure, etc.) and develop a general perception about the events.

• Experiment:

Go to the SOCR Experiments [[1]] and select the Ball and Urn Experiment from the drop-down list of experiments on the top left. The image below shows the initial view of this experiment:

To the left of the “update/stop” selections are four buttons that represents the beginning and end of the experiment. The play button will display the data after one trial has been completed and the fast forward button will displace the data after a specific number of trials have been performed. The stop button will cease the experiment and the reset button will clear all data information gathered.

The “update” selection allows the experimenter to modify the trials in which the data after 1, 10, 100, or 1000 trials have been performed. The “stop” selection determines the maximum number of trials to be carried out during the experiment.

The larger the value of n is, the more data will be collected. The outcome of the experiment is dependent upon p in which the larger the value p is, the more heads will appear and the smaller the value of p is, the less number of heads will appear. This is illustrated in the image below:

• Applications:

The coin sample experiment is significant for random, categorical variables that may be represented by the Bernoulli distribution [[2]]. For instance, the probability that it may rain on a given day of the week in a selected area may be determined, where n will represent the number of days in the week, x will represent the day that it will rain, and p will represent the probability of rain in the location. The SOCR Coin Sample Experiment allows us to simulate this natural phenomenon on the computer.