Question: please kindly help me solve this as numbered Question 1 (a) Consider a general birth-death process with birth rate and death rate uin state i

please kindly help me solve this as numbered

Question 1 (a) Consider a general birth-death process with birth rate and death rate uin state i (i=0, 1, 2, ...). What are the detailed balance equations for this process? (b) Derive the steady-state distribution for the general birth-death process considered in part (a). What are the conditions for the steady-state distribution to exist? Question 2 Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today. (1) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather. (ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix

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