=+where is a positive constant; and (iii) the process has independent increments; that is, for any

=+where λ is a positive constant; and (iii) the process has independent increments; that is, for any n > 1 and 0 ≤ t0 < t1 < ··· < tn, the random variables P(tj ) − P(tj−1), j = 1,...,n, are independent. The constant λ is called the 312 9 Time and Spatial Series strength of the Poisson process. Derive the mean and variance of P(t) and show that n = P(n + 1) − P(n) − λ, n = 1, 2,..., is a WN(0, λ) process.