A game involving chance is said to be a fair game if the expected amount won or lost is zero. Consider the following arcade game. A player pays $1 and chooses a number from 1 to 10. A spinning wheel...

A game involving chance is said to be a fair game if the expected amount won or lost is zero. Consider the following arcade game. A player pays $1 and chooses a number from 1 to 10. A spinning wheel then randomly selects a number from 1 to 10. If the numbers match, the player wins $5. Otherwise the player loses the $1 entry fee.

(a) Define a random variable
 that is the amount won by the player and draw its probability distribution. (Capital letters other than
 can be used for random variables.) Use negative values for losses, and positive values for winnings.

(b) Find the mean of
. Is this a fair game?