For a positive integer n, let τ (n) = (2 k , i), where i is the remainder when we divide n by 2k, the largest possible power of 2. For example, τ (10) = (2 3 , 2), τ (12) = (2 3 , 4), τ (19) = (2 4 ,...

For a positive integer n, let τ (n) = (2^k, i), where i is the remainder when we divide n by 2k, the largest possible power of 2. For example, τ (10) = (2³, 2), τ (12) = (2³, 4), τ (19) = (2⁴, 3), and τ (69) = (2⁶, 5). In an experiment a point is selected at random from [0, 1]. For n ≥ 1, τ (n) = (2^k, i), let