4. DIGIT PATTERNS 1 Consider a stream of decimal digits which appear to be randomly distributed...
4. DIGIT PATTERNS 1 Consider a stream of decimal digits which appear to be randomly distributed according to a Benford distribution, modified to include the digit "O": d Pr(D) 0 0.27894 0.16317 2 0.11577 3 0.08980 4 0.07337 5 0.06203 0.05374 7 0.04740 0.04240 9 0.03836 10 0.03502 (a) What are the expected time and variance to observe the digit sequence "007" ? 6 8 (b) The decimal digits of pi (pi) are thought to be random and uniformly distributed. If this is so, what are the expected time and variance to observe a digit repeated 3 times, e.g. "111" or "666" ?