A game consists of drawing tickets with numbers on them from a box, independently with replacement. In order to play you have to stake $2 each time you draw a ticket, your net gain is the number on the ticket you draw, suppose there are 4 tickets in the box with numbers -2, - 0, 3 on them. If, for example the ticket show $3 then you get your stake back, plus an additional $3.
a) Let X stand for your net gain in one game. What is the distribution of X? Find E(X) and Vαr(X).
b) If you play 100 times, what is your chance of winning $25 of more?