In this work we study the some general fractal sums of pulses defined in R by:where (a n ), (λ n ) two positive scalar sequences such that a n is divergent, and (λ n ) is non-increasing to 0, G is an elementary bump and X n are independent random variables uniformly distributed on a sufficiently large domain Ω. We investigate the Hausdorff dimension of the graph of G and in particular we answer a question given by Tricot in (Courbes et dimensions fractales, Springer, Berlin, 1995).