Question: 6.1.2 A pure birth process starting from X.0/ D 0 has birth parameters 0 D 1; 1 D 3;2 D 2, and 3 D 5.

6.1.2 A pure birth process starting from X.0/ D 0 has birth parameters 0 D 1;

1 D 3;2 D 2, and 3 D 5. Let W3 be the random time that it takes the process to reach state 3.

(a) Write W3 as a sum of sojourn times and thereby deduce that the mean time is E[W3] D 11 6 .

(b) Determine the mean of W1 CW2 CW3.

(c) What is the variance of W3?

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