Question: Probability & Stochastic Proc 4. [1' marks] A machine is subject to shocks which occur according to a Poisson process of rate A :5- 0.

Probability & Stochastic Proc

4. [1' marks] A machine is subject to shocks which occur according to a Poisson process of rate A :5- 0. 'When a shook occurs, it is fatal with probability p E {0,1}, and the machine fails. When the machine fails, it. is immediately replaced by an identical machine. Consider the continuoustune Ml'km' Chain {XL t E H}, where X(t} is the nurnher of shocks that the current machine has survived at time t. a} [5 marks] Determine the stationary.r distlibution of this chain

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