LetS_{1},S_{2},⋯ be the occurrence times of a homogeneous Poisson Process with counting ProcessN(t) and waiting timesX_{1},X_{2},⋯ . True or False:

a) For any i<j, X_{j}is independent of S_{i}

b) For any i<j, X_{i }is independent of S_{j }

c) For any i≠j, S_{i}is independent of S_{j }

d) For any T > S_{i}, N(T) - N(S_{i}) = 0 if and only if S_{i+1 }> T

WhereTis our index set oft, essentiallyTis the total number of events