Average the reciprocal score and distinguish gains from guesses

Two unbiased regular tetrahedral dice have faces 1,2,3,4. The number on the face in contact with the table is recorded. Tom throws both and notes their total X. Harry guesses the total; his guess is Y. If correct, Harry wins $Y^2$ dollars; otherwise he loses $Y/2$ dollars.

(i) Obtain the distribution of X and find $E(1/X)$ correct to 3 decimal places.4 marks

(ii) Harry guesses 6 in a particular game. Find his expected gain.2 marks