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Consider rolling a 6-sided die. The outcome of interest is the number of dots that appears on the topside when the die stops rolling. The possible outcomes are 1, 2, 3, 4, 5 & 6. Suppose we play the following game. Roll the 6-sided die, you are rewarded a dollar amount equal to the number of dots on the topside of the die when it comes to rest. Suppose the die is fair (each side is equally likely). Define the random variable X to be the amount you are rewarded after one roll.

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Using the discrete probability relation, the random variable, X for the amount to be rewarded per roll is :

  • X : ___ 1___ 2 ___ 3 ___ 4 ___ 5 ___6
  • P(X)__1/6__ 1/6 __ 1/6__ 1/6___ 1/6 _ 1/6

The dollar amount corresponds to the number on the die :

Possible amount awarded (X) :

  • X = {1, 2, 3, 4, 5, 6}

Since we have a fair die :

Probability of obtaining any certain value on the die is the same ; Hence, the probability of obtaining a certain value would be :

  • P = 1/6

Hence, the random variable, X can be defined thus:

  • X : ___ 1___ 2 ___ 3 ___ 4 ___ 5 ___6

  • P(X)__1/6__ 1/6 __ 1/6__ 1/6___ 1/6 _ 1/6

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