An instant lottery ticket costs $2. Out of a total of 10,000 tickets printed for this lottery, 250 tickets contain a prize of $5 each, 125 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. X P(x) Determine the mean and standard deviation of x. Round your answers to two decimal places. Mean = $ i gain Standard deviation = $ lose On average, the players who play this game are expected to = $ per ticket with a standard deviation of $