Hey Rorschach27.
In terms of independence, we define this as P(A=a,B=b) = P(A=a)*P(B=b). In other words, if you have the joint distribution and can separate it in terms of this product, then you have proven that both processes are independent.
Let S_{1},S_{2},⋯ be the occurrence times of a homogeneous Poisson Process with counting Process N(t) and waiting times X_{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
Where T is our index set of t, essentially T is the total number of events
Hey Rorschach27.
In terms of independence, we define this as P(A=a,B=b) = P(A=a)*P(B=b). In other words, if you have the joint distribution and can separate it in terms of this product, then you have proven that both processes are independent.