Let W be a random variable giving the number of heads minus the number of tails in three tosses of a coin.

a) List all the possible values of the random variable W. [2 marks]

b) Find the probability distribution of W, assuming that the coin is biased so that a head is twice as likely to occur as a tail. [4 marks]

c) Find the expected value and variance of W using the distribution obtained in (b) above.