I need to fuel my car every week. Based on my observation, the price of gas...

I need to fuel my car every week. Based on my observation, the price of gas really follows a Markov Chain. The price can be 3.2 dollars, 3.3 dollars or 3.4 dollars for one gallon. If the price for this week is 3.2 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability of 0.4, 0.4 and 0.2 respectively. If the price for this week is 3.3 dollars, the price of next week will be 3.2, 3.3 and 3.4 with the probability for 0.2, 0.5 and 0.3 respectively. If the price for this week is 3.4 dollars, the price of next week will be 3.2, 3.3 and 3.4 with probability 0.3, 0.3 and 0.4 respectively.
1. Please give out the transition matrix.
2. For one year, how much should I pay for the gas for my car? (Assume 52 weeks/year and I use 10 gallons every week).
3. If the price of this week is 3.2 dollars, what is the probability that I will observe 3.3 dollars price after 2 weeks?

If the price of this week is 3.2 dollars, I will observe 3.3 dollars price for the first time after how many weeks in average?

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Expert Solution

orchestra answered 1 year ago

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