Variables may be discrete or continuous. A continuous variable can be any number including decimals/fractions — for example, buying ground beef at the butcher’s counter of the grocery store involves a continuous variable. A person could buy 3.58 pounds of ground beef, 2 1/2 pounds, or some other portion of a pound. A discrete variable, however, is limited to integer values. An example from the grocery store is buying canned vegetables. It is impossible to buy 1/2 a can, or similar fractions, because the can is a unit which must stay intact. Only integer values are valid.
The virtual die rolling experiment was carried out, and a graph of the results is attached. Although the probability of rolling a particular number should always be 1/6, the results from 20 rolls were more variable than that. Some numbers, such as 5, were obtained only 2 times, while the number 2 was obtained 5 times. If the die had been rolled many more times — 100 times, or 500 times — the probabilities of each number would have moved towards 1/6 (unless there was a problem with the virtual die rolling program).
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"Random Variables: Rolling a Die".
The random variable in this experiment is the number shown on the die. It is a discrete variable because it is limited to the integers 1-6. There is no way to roll any other integer (such as 12) without adding additional dice, and there is no way to roll any fractions or decimals such as 6.1 or 3 1/3 (Grinstead & Snell, 2010).
The table of these results is a probability distribution because a probability distribution is a table or equation that connects each possible value of a statistical experiment with its likelihood or probability of occurring. In this experiment the probabilities are not uniform. Theoretically, when a die is rolled, the probability that any given number will result is 1/6. However, as mentioned above, a limited number of trials may not result in the uniform distribution that is expected (Grinstead & Snell, 2010).
This is not a binomial distribution because there are more than two possible outcomes. Flipping a coin results in a binomial distribution because the outcome can be only heads or tails.
- Grinstead, C., & Snell, L. (2010). Introduction to Probability. Retrieved from http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html
