Note for future revision. X = Inter arrival time = Time to first arrival = Time to next arrival (as each is independent). PDF of X ~ Exp(λ) Sn = Time to n-th arrival = Accumulated inter arrival times, Xes, up to n-th arrival = X1 + X2 + ... + Xn. PDF of Sn ~ G(n,λ) = Gamma Distribution
@@StatCourses could you please tell the reference material and books you used. This is the best explanation on how gamma distribution arises. I haven't found any text book which explains this clearly.