Question

Problem 7. Define an (infinite) binary sequence S infinitely many i0,h that un! S 10,1j to be prefir-repetitive if there are Prove: If the bits of a sequence S 0,10 are chosen by independent tosses of a fair coin, then

Answer 1

Answer:

Probability that the first two toss results in {0, 1}, is 1/2 Similarly, the probability that two tosses result in {0, 1}^2 = 1/2^2 Likewise, the probability that three tosses results in {0, 1} ie probability that s = {0, 1}^3 = 1/2^3 . Similarly, probability that infinite consecutive tosses will result in {0, 1}, ie .probability that s = {0, 1}^infinity = 1/2 infinity = 1/infinity = 0 Hence, probability [s is prefix - repetitive] = 0