Determine the variance, Basic Statistics

A gambling machines works in the following way. The player inserts a penny into 1 of 5 slots which are colored Blue, Red, Orange, Yellow & Green corresponding to 5 colored light bulbs. The player can choose which ever colored slot he likes. After the penny has been inserted 1 of the 5 bulbs lights up. If the bulb lit up is the same color as the slot selected by the player, then the player wins and receives from the machine R pennies, where P(R=2)=1/2, P(R=4)=1/4, P(R=6)=3/20, & P(R=8)=P(R=10)=1/20 If the color of the bulb lit up and the slot selected are not the same, the player receives nothing from the machine. In either case the player does not get back the penny that he inserted. Assuming that each of the colors is equally likely to light up and that the machines selects the bulbs at random, determine (c ) the variance of the amount gained by the player from a single try.

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