In this paper, we consider random words ω₁ω₂ω₃⋯ω_n of length n, where the letters ω_i ∈ℕ are independently generated with a geometric probability such that P{ω_i=k}=pq^k-1 where p+q=1 . We have a descent at position i whenever ω_i+1 < ω_i. The size of such a descent is ω_i-ω_i+1 and the descent variation is the sum of all the descent sizes for that word. We study various types of random words over the infinite alphabet ℕ, where the letters have geometric probabilities, and find the probability generating functions for descent variation of such words.