MathDB
2019 BMT Individual 8

Source:

January 9, 2022
algebra

Problem Statement

Let ϕ=12019\phi =\frac{1}{2019}. Define gn={0 if    round(nϕ)=round    ((n−1)ϕ)1 otherwise..g_n =\begin{cases} 0 & \text{ if} \,\,\,\, round (n\phi) = round \,\,\,\, ((n - 1)\phi) \\ 1 & \text{ otherwise} .\end{cases}. where round (x)(x) denotes the round function. Compute the expected value of gng_n if nn is an integer chosen from interval [1,20192][1, 2019^2].
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