<PRE><B>Question 860902</B>
A)Student says that the die is a 6 sided die 
our sample space consists of pairs (a, b) where a is 0 or 1 depending on the coin toss (1 = heads, 0 = tails) and b is 1, 2, 3, 4, 5, 6 depending on die toss, we assume the die has 6 sides and each side is numbered
here is the sample space 
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6)
there are 12 possible outcomes when throwing the coin and dice
S(X) is 1 if coin toss is heads
S(X) is 0 if coin toss is tails
S(Y) is i if die toss is i, where i is 1, 2, 3, 4 5, 6
B) sample space for Z when Z = XY
Z value    probability
  1           1/12
  2           1/12
  3           1/12
  4           1/12
  5           1/12
  6           1/12
  0           6/12 = 1/2
adding up the probabilities we get 1/2 + 1/2 = 1
C) E(z) = 0*(1/2) + 1*(1/12) + 2*(1/12) + ...+6*(1/12)
   E(z) = 0 + (1/12)*(1 + 2 + 3 + 4 + 5 + 6)
   E(z) = (1/12) * 21 = 21/12 = 7/4 = 1.75
Var(Z) = (0 - 21/12)^2 * (1/2) + (1 - 21/12)^2 * (1/12) + (2 - 21/12)^2 * (1/12) + ... + (6 - 21/12)^2 * (1/12)
Var(Z) = (0 - 1.75)^2 * (1/2) + (1/12) * ( (1 - 1.75)^2 + (2 - 1.75)^2 + (3 - 1.75)^2 + (4 - 1.75)^2 + (5 - 1.75)^2 + (6 - 1.75)^2 )
Var(Z) = 1.53125 + (1/12) * 35.875 = 4.52

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