Final answer:
The random variable X signifies the amount of matches in a dice game connected with Chinese and Vietnamese New Year, taking on values 0 to 3 to determine profit in the game.
Step-by-step explanation:
The random variable X in the context of the Chinese and Vietnamese New Year dice games represents the number of matches between the dice roll and the player's bet. The values that X can take on are, namely, 0 (no matches), 1 (one match), 2 (two matches), and 3 (three matches). As for its distribution, X follows a probability distribution where each possible value of X has an associated probability based on the rules described for profit per game. If X = 0, the player loses their $1 bet; X = 1 results in a $1 profit; X = 2 results in a $2 profit; and X = 3 yields a $3 profit. This distribution shows that the outcome of playing the game is not solely determined by chance but also the chosen number or object to bet on.