3a&b Sec. 1.3 Markov Chains and Dynamic Models 3. In the frog Markov chain, what

Question

3a&b Sec. 1.3 Markov Chains and Dynamic Models 3. In the frog Markov chain, what is the probability distribution in the next period if the current distribution is (a) p3 = 1, all other p, 0? (b) P2 = .5, p, = .5, all other p, = 0? (c) P2 = .25, p,-25, p4-5, all other pi-0? 4. The printing press in a newspaper has the following pattern of break- downs. If it is working today, tomorrow it has 90% chance of working (and 10% chance of breaking down). If the press is broken today, it has a 60% chance of working tomorrow (and 40% chance by being broken again). (a) Make a Markov chain for this problem; give the matrix of transition probabilities and draw the transition diagram. i 50 50chance of the press working today, what are the

Explanation / Answer

Answer:

Given that information ,

Lose the next game =1/3, then win the next game= 1/2

win the next game = 2/3, then win the next game =2/3

Now, win the game after next game = (1/3)(1/2)+(2/3)(2/3)

= (1/6)+(4/9)

= 0.6111

   Therefore, 0.6111 chance they win the game after the next game.

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