Assignment 5
统计作业代写 i.e. the random times spent in each state before moving and also the probabilities of where the moves go to on leaving each state.
To be handed in no later than 12 noon on Thursday 9 November
This contributes 10% to the overall mark
For a continuous time Markov process on states {1, 2, 3}, the rate matrix
for some λ > 0. The process starts at 2; i.e. X(0) = 2. 统计作业代写
1.State the distribution for the number of changes in the process by time t. Explain the answer, for which you can use a result we obtained in class for the Poisson process.
2.Describe the process in full; i.e. the random times spent in each state before moving and also the probabilities of where the moves go to on leaving each state.
3.The stationary probability vector π satisfies π P(t) = π for all t. Show that for such π it is that π G = 0. Recall that
P(t) = e tG = I + tG + t 2G 2 /2! + t 3G 3 /3! + · · · . 统计作业代写
4.Find the π for the given G.
5.If an observer is watching the outcome of the process at an arbitrarty large time point t, what is the probability the observer sees the state 3 at that time.
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