Limit distribution of ascent, descent or excedance length sums of permutations

Let An(σ) denote the sum of the lengths of ascents of a permutation σ of {1, ..., n} chosen uniformly at random. We find the exact expectation and variance and prove a central limit theorem for the An. Identical results hold for the sum of the lengths of descents or of excedances of a permutation of {1,..., n} chosen uniformly at random.