The federal government tries to boost small business activities by awarding annu

Question

The federal government tries to boost small business activities by awarding annual grants for projects. All bids are competitive but the chance of receiving a grant is highest if the owner has not received any during the last three years and lowest if awards were given in each of the last three years. Specifically, the probability of getting a grant if none were awarded in the last 3 years is 0.9. It decreases to 0.8 if one grant was awarded, 0.7 if two grants were awarded, and only 0.5 if three were received. (a) Describe this situation as a Markov chain by completing the 1-step transition matrix. Remember to clearly define your states. (b) Determine the expected number of awards per owner per year

Explanation / Answer

there are 4 states, probability of wninning no award, when either 0, 1,2 or 3 awards were won in last 3 years.

probability of wninning one award, when either 0, 1,2 or 3 awards were won in last 3 years.

probability of wninning two awards, when either 0, 1,2 or 3 awards were won in last 3 years.

probability of wninning three awards, when either 0, 1,2 or 3 awards were won in last 3 years

Part II

0 1 2 3 0 0.1 0.2 0.3 0.5 1 0.9 0.8 0.7 0.5 2 0 0 0 0 3 0 0 0 0

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