In getting crowd for a consumer exhibition, the organizer runs a lucky draw during the event. Out of a total of 5,000 tickets printed for this lucky draw, 500 tickets contain a prize worth $5 each, 50 tickets have a prize worth $10 each, 5 tickets have a prize worth $1000 each, and 1 ticket has a prize worth $10,000. Let x be the random variable that denotes the value of prize a participant may win by playing this lucky draw.

a) Compute the probability distribution of x, P(x).

b) Determine the mean and standard deviation of x.

c) If the entrance fee to the exhibition costs $2, what is the expected gain by each participant who join the lucky draw of this event.