Set A consists of the ten digits 0, 0, 0, 0, 0, 0, 2, 2, 2, 4.
Set B consists of the seven digits 0, 0, 0, 0, 2, 2, 2.
One digit is chosen at random from each set. The random variable X is defined as the sum of these two digits.
i. Show that P(X = 2) = 3/7.
ii. Tabulate the probability distribution of X.
iii. Find E(X ) and Var(X ).
iv. Given that X = 2, find the probability that the digit chosen from set A was 2.
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