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Math Help - True/False: Occurrence Times, Counting Process and Waiting Times

  1. #1
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    True/False: Occurrence Times, Counting Process and Waiting Times

    Let S1,S2, be the occurrence times of a homogeneous Poisson Process with counting Process N(t) and waiting times X1,X2, . True or False:

    a) For any i<j, Xj is independent of Si
    b) For any i<j, Xi is independent of Sj

    c) For any ij,
    Siis independent of Sj

    d) For any T > Si, N(T) - N(Si) = 0 if and only if Si+1 > T

    Where T is our index set of t, essentially T is the total number of events
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  2. #2
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    Re: True/False: Occurrence Times, Counting Process and Waiting Times

    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.
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