EXAMPLE 1Notation for random variables

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Suppose our experiment is to toss a single fair die, and we are interested in the number rolled. We define our random variable to be the outcome of a single die roll.

  1. Why is the variable a random variable?
  2. What are the possible values that the random variable can take?
  3. What is the notation used for rolling a 5?
  4. Use random variable notation to express the probability of rolling a 5.

Solution

  1. We don't know the value of before we toss the die, which introduces an element of chance into the experiment, thereby making a random variable.
  2. The possible values for are 1, 2, 3, 4, 5, and 6.
  3. When a 5 is rolled, then equals the outcome 5, and we write .
  4. Recall from Section 5.1 that the probability of rolling a 5 for a fair die is 1/6. In random variable notation, we denote this as .