Complete the following:
Markov Processes
1. For a situation with weekly dining at either an Italian or Mexican restaurant,
a. the weekly visit is the trial and the restaurant is the state.
b. the weekly visit is the state and the restaurant is the trial.
c. the weekly visit is the trend and the restaurant is the transition.
d. the weekly visit is the transition and the restaurant is the trend.
2. The probability of going from state 1 in period 2 to state 4 in period 3 is
a. p12
b. p23
c. p14
d. p43
3. The probability a system is in a particular state after a large number of periods is
a. independent of the beginning state of the system.
b. dependent on the beginning state of the system.
c. equal to one half.
d. the same for every ending system.
4. The daily price of a farm commodity is up, down, or unchanged from the day before. Analysts predict that if the last price was down, there is a .5 probability the next will be down, and a .4 probability the price will be unchanged. If the last price was unchanged, there is a .35 probability it will be down and a .35 probability it will be up. For prices whose last movement was up, the probabilities of down, unchanged, and up are .1, .3, and .6.
a Construct the matrix of transition probabilities.
b. Provide a system of equations for calculating the steady state probabilities.