Question

BENFORD 25 POINTS (A) 5 POINTS Characterize all numbersエso that 1000 has leading digit 9. (B) 5 POINTS What is the leading digit of We pointed out before that there can be ambiguity in these sorts of expressions so think of this as the result of the following recursive definition of a sequence (B)where the above is just B (C) 15 POINTS Suppose we form random numbers in the following way Pick a random digit in 0,1,2,3,4,5,6,7,8,9) with each choice equally likely If the digit is a 9 then choose a random number w uniformly in [0,0.9). Uniformly just means that all possibilities are equally likely. If the digit is not a 9 then choose w uniformly in 0.9, 1 . Compute Z 10+3 What is the maximum and what is the minimum that Z can be? Determine the frequeney of each possible leading digit for Z. Give each frequency accurate to 6 decimals (eg, as in 17.6091% which is the BENFORD percentage for leading digit 2).

Answer 1

3 Jovgnes 22 +20 11 - 3 8 53-24- =29. 600