a. State in a table the probability distribution for the outcome of rolling a balanced die. (This is called the uniform distribution on the integers 1, 2,., 6.)
b. Two balanced dice are rolled. Show that the probability distribution for X = total on the two dice is as shown in the figure. (First construct the sample space of the 36 equally likely outcomes you could get. For example, you could denote the six outcomes where you get a 1 on the first die by (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), where the second number in a pair is the number you get on the second die.)
c. Show that the probabilities in part b satisfy the two conditions for a probability distribution.
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0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 002 10 12