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Omni-MATH / Values a₁,…,a₂₀₁₃ are chosen independently and at random from the set {1,…,2013}. What is expected number of distinct values in the set {a₁,…,a₂₀₁₃} ?

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problem

Values a1,…,a2013a_{1}, \ldots, a_{2013} are chosen independently and at random from the set {1,…,2013}\{1, \ldots, 2013\}. What is expected number of distinct values in the set {a1,…,a2013}\{a_{1}, \ldots, a_{2013}\} ?
Plain-text mathematical notation (without MathML)
Values a₁,…,a₂₀₁₃ are chosen independently and at random from the set {1,…,2013}. What is expected number of distinct values in the set {a₁,…,a₂₀₁₃} ?
Original LaTeX notation
Values $a_{1}, \ldots, a_{2013}$ are chosen independently and at random from the set $\{1, \ldots, 2013\}$. What is expected number of distinct values in the set $\{a_{1}, \ldots, a_{2013}\}$ ?

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Source and history

task_id
71ca0461-9ac9-5ec1-a736-b7cbe5953ae9
task_key
test--71ca0461-9ac9-5ec1-a736-b7cbe5953ae9
task_revision_id
1
config / split
/ test

Official source

initial import