Consider rolling a 6-sided die. The outcome of interest is the number of dots that appears on the top side 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. X = dollar amount rewarded after one roll Answer the following questions: What are the possible values the random variable, X, can take on?  Explicitly write out the probability mass function (pmf) for the random variable X.  Write out explicitly the cumulative distribution function (cdf) for the random variable X.  What is the ‘typical’ amount awarded when playing this game?  How much does the amount awarded vary around the value obtained in part (4)?

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A:

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A: From the provided information is  E(X)=-2*P(X=-2)+p*P(X=p)E(X)=-2*45+p*150=-85+p50=-8+pp=8

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