Question

In: Statistics and Probability

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).

  1. What is the probability that it will not start 5 days from now if it started today?

  2. What is the probability that it will not start 5 days from now if it did not start today?

  3. What is the probability that it will start in the long run if the matrix of transition probabilities does not change?

Solutions

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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%.


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