An instant lottery ticket costs $2. Out of a total of 10,000 tickets printed for this lottery, 750 tickets contain a prize of $5 each, 50 tickets have a prize of $10 each, 4 tickets have a prize of $1000 each, and 1 ticket has a prize of $5000. Let x be the random variable that denotes the net amount a player wins by playing this lottery.

Write the probability distribution of x.

Enter the exact answers. Enter your answers for x in increasing order.

Determine the mean and standard deviation of x.

On average, the players who play this game are expected to (Choose your answer: gain or lose) $__ per ticket with a standard deviation of $__.