a) Calculate E(X) and E (1/X).

X 1 2 3 4 p(x) 0.4 0.3 0.2 0.1

b) In a win-win game, the player will win a monetary price, but he/she has to decide between a fixed and a random price. In particular the player is offered $1000/E(X) or $1000/X, where the random variable X has the distribution given above. When the choice is made, a value of X is generated and the player receives the chosen price. Which choice (strategy) would you recommend the player to make?