Question: 1.2. A pure birth process starting from X(O) = 0 has birth parameters ,, = 1, A, = 3, A, = 2, A, = 5.

1.2. A pure birth process starting from X(O) = 0 has birth parameters

,, = 1, A, = 3, A, = 2, A, = 5. Let W, be the random time that it takes the process to reach state 3.

(a) Write W, as a sum of sojourn times and thereby deduce that the mean time is E[W] = 6.

(b) Determine the mean of W, + W, + W.

(c) What is the variance of W,?

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