Q. Let us consider that, {Xn} is a Markov chain with 5 states 0, 1, 2, 3 and 4. Suppose, Po4 =1 and when the state is in the state i, i > Othe next is equally likely to be in any of the states 0, 1, 2. . i – 1 a. What is the nature of the states of this Markov chain. b. Find whether there exists a limiting distribution of this this Markov chain and compute that if it exists.

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A: The solution is given below in the next step:

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A:

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A:

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A:

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A: Explanation of the solution is given below...

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A: The solution is given in the next step.

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Q: 16 2/5- 8 4/9

A:

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A:

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A: Solution: The objective is to find the value of the given expression

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A: Given

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A:

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A: Here we find Laplace inverse transform

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A:

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A:

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A: Cube means multiplying three times:   563=56×56×56=5×5×56×6×6=5363=125216

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A:

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A: Given,

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A: Using By Parts rule of integration.