If one has a fair coin, he can generate his own table of random numbers in the following manner: let Xi = 1 if the coin comes up heads on the first toss, and x\ = 0 if it comes up tails. Similarly, let X2 = 1 if it comes up heads on the second toss and let x2 = 0 if it comes up tails. Define X3 and x4 similarly for the third and fourth toss. Now toss the coin four times, and find y = x1 + 2x2 + 4x3 + 8x4.

List the possible values of y and the probabilities for the different values.

Would you call y a random number? Suppose that you simply ignored values of y of 10 or greater. Would the resulting numbers be random digits?