I would like to know how to solve this problem using POM or Excel Alan Resnik,...

I would like to know how to solve this problem using POM or Excel

Alan Resnik, a friend of Ray Cahnman, bet Ray $5 that Ray’s car would not start 5 days from now (see Problem 14-8).

What is the probability that it will not start 5 days from now if it started today?
What is the probability that it will not start 5 days from now if it did not start today?
What is the probability that it will start in the long run if the matrix of transition probabilities does not change?

Solutions

Expert Solution

I have answered the question below

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Answer:

(a)

If: p(0) = (1 0), p(1) = (0.9, 0.1), p(5) = (0.76944, 0.23056)

Probability that it will not start in five days from today is 23.056%.

(b)

If: p(0) = (0 1), p(1) = (0.3, 0.7), p(5) = (0.69168, 0.30832)

Probability that it will not start five days from today is 30.832%

(c)

Markov Analysis Results above: In equilibrium p = pP

p₁ = 0.9p₁ + 0.3p₂ p₂ = 0.1p₁ + 0.7p₂ p₁ + p₂ = 1 or, p₁ = 0.75, p₂ = 0.25

Therefore, long-run probability of starting is 75%.

orchestra answered 1 year ago

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