Suppose that you pay $3 to play a game. The following is the instruction of the game. First, you toss two fair coins independently. If you observe two heads, then you will earn $8. Otherwise, you will earn nothing (e.g. $0) . let X be your net earning of the game. Note that your net earning is given by the amount of money you earn from the game minus the amount of money you pay for the game.

Part A Determine the probability distribution of X by completing the table below. Note Put all X values in an increasing order and round the probabilities to 5 decimal places (0.12345) if possible )

X	Probability

Part B Calculate the expected value of X. (Round the expected value to 5 decimal places if possible)

Part C Calculate the standard deviation of X (Round the standard deviation to 5 decimal places if possible)