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In this paper we study the distribution of the size of the value set for a random polynomial with degree at most q-1 over a finite field F_q. We obtain the exact probability distribution and show that the number of missing values tends to a normal distribution as q goes to infinity. We obtain these results through a study of a random r-th order cyclotomic mappings. A variation on the size of the union of some random sets is also considered.arXiv:1407.5884v1 fatcat:mc34txft2rgf7afqg7qkoioi2m