The i-th digit Xi, in the binary expansion of a randomly chosen number in the interval [0, 1] is

a Bernoulli (0.5) random variable and X1, X2, . . . is a sequence of iid random variables.

(a) Use the Central Limit Theorem to approximate the probability that a randomly

chosen number in the [0, 1] interval has more than 128 zeros in the first 512 digits of its binary

expansion.

(b)Use the De Moivre-Laplace Formula to approximate the probability of the event

mentioned in part (a).