Let's say you decide to play Rock/Paper/Scissors with a friend. Every round you choose either Rock, Paper or Scissors and show your friend. Outcomes can be defined as "win", "lose", "draw". Rock will win against Scissors, Scissors will win against Paper and Paper will win against Rock. If you both play the same thing you tie and no one wins. Assume independence between rounds.

a) Assume X is a random variable with outcomes given by one round of Rock/Paper/Scissors as described above. Sketch the X distribution and indicate the type of distribution. (Note: draw the PDF)

b) Based on the last part, now assume Y is a random variable with only two outcomes (winning'' and not winning'') from one game of Rock/Paper/Scissors. Sketch the Y distribution and indicate the type of distribution along with its mean and variance. (Note: draw the PDF)

c) Based on the last part, now assume C is a random variable defined by C=Y+Y+Y+Y. Sketch the C distribution and indicate the type of distribution along with its mean and variance. (Note: draw the PDF)