Starting at value 0, the fortune of an investor increases per week by 200 with probability 3/8, remains constant with probability 3/8 and decreases by 200 with probability 2/8. The weekly increments...

Starting at value 0, the fortune of an investor increases per week by

200 with probability 3/8, remains constant with probability 3/8 and decreases by

200 with probability 2/8. The weekly increments of the investor's fortune are assumed to be independent. The investor stops the 'game' as soon as he has made a total fortune of

2000 or a loss of
1000, whichever occurs first.

By using suitable martingales and applying the optional stopping theorem, determine

(1) the probability p that the investor finishes the 'game' with a profit of
2000, 2000

(2) the probability p that the investor finishes the 'game' with a loss of
1000, −1000

(3) the mean duration of the 'game'.