Random Variable

Definition of Random Variable

• A random variable is a function that assigns numeric values to the outcomes of an experiment. In general, a random variable is written as a capital X or Y etc.

              

Examples of Random Variable

• A random variable can be used to describe the experiment of flipping coins and the possible outcomes.

For example, in the experiment of flipping four coins, we could define random variable X to equal the number of tails that result. In this case, the possible values of X would be 0, 1, 2, 3, or 4.

Solved Example on Random Variable

Two dice are rolled. A random variable X is defined as the sum of the two faces. If a 3 and 5 show up when the dice are rolled, then X = 8, that is the value assigned to this outcome is 8. Find all the possible values of the random variable X in this experiment.

Choices:

A. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

B. {3, 4, 5, 6, 7, 8, 9, 10, 11}

C. {1, 2, 3, 4, 5, 6}

D. none of these

Correct Answer : A

Solution:

Step 1: When a die is rolled the possible outcomes are {1, 2, 3, 4, 5, 6}.

Step 2: The random variable X is defined as the sum of the two faces. The minimum value of the sum is given by the pair (1, 1) and the maximum value of the sum is given by the pair (6, 6).

Step 3: So, the possible values of the random variable X are {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

                  

Related Terms for Random Variable

• Experiment
• Function
• Outcome

 

Additional Links for Random Variable

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