Suppose a small tin box contains marbles of the same size and weight but of various colors: 5 Red, 3 Black and 2 Gold. You play a simple game in which you may win or lose money after randomly selecting 2 marbles without replacement from the tin box. Let random variable "X" be defined as the amount of money won or lost when two marbles are randomly selected without replacement from the small tin box. You win $10 if you select a Gold marble; you win $1 if you select a Black marble, and you lose $5 if you select a Red marble.

a) In space below, list the Sample Space for this game. Also find the probability of each of the outcomes listed in your Sample Space. Use exact values [fractions] for the probabilities. Tree diagram is not necessary!

b) For the marble game and random variable X defined above, construct a TABLE to describe the probability density function f(x) and the cumulative distribution function. Then use your Table to derive Expected Value of X, also Variance and Standard Deviation. Show all work! (Solve amounts of money to the nearest penny.)