Question

In: Statistics and Probability

Problem 1 Whether the stock goes up tomorrow depends upon whether it increased today and yesterday....

Problem 1

Whether the stock goes up tomorrow depends upon whether it increased today and yesterday. If the stock increased today and yesterday, it will decrease tomorrow with probability α1 . If the stock increased today and decreased yesterday, it will decrease tomorrow with probability α2. If the stock decreased today and increased yesterday, it will decrease tomorrow with probability α3. Finally, if the stock decreased today and yesterday, it will decrease tomorrow with probability α4.

a) Define the states for a Markov chain that represent this system.

b) Construct the (one-step) transition matrix of the Markov chain.

c) Explain why the states used for this Markov chain cause the mathematical definition of the Markovian property to hold even though what happens in the future (tomorrow) depends upon what happened in the past (yesterday) as well as the present (today).

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Problem 2 Reconsider Problem 1. Suppose now that whether or not the stock goes up tomorrow...
Problem 2 Reconsider Problem 1. Suppose now that whether or not the stock goes up tomorrow depends upon whether it increased today, yesterday, and the day before yesterday. a) Can this problem be formulated as a Markov chain? b) If so, what and how many are the possible states? c) Explain why these states (the ones defined in part b) give the process the Markovian property whereas the states in Problem 1 do not (for this problem). Problem 1 Whether...
Suppose that the chance of rain tomorrow depends on previous weather conditions only through whether or...
Suppose that the chance of rain tomorrow depends on previous weather conditions only through whether or not it is raining today and not on past weather conditions. Suppose also that if it rains today, then it will rain tomorrow with probability 0.6, and if it does not rain today, then it will rain tomorrow with probability 0.3, then a. Calculate the probability that it will rain four days from today given that it is raining today. b. What is the...
If 180 is increased by 55%, what is the result? Shona ate 100 grapes yesterday. Today...
If 180 is increased by 55%, what is the result? Shona ate 100 grapes yesterday. Today she eats 90% more than yesterday. How many grapes did she eat today? John took 140 photographs last month. This month he took 85% more. How many photographs did he take this month? What number is 75% more than 80? Increase 950 by 10%. Last time Orange Floyd released an album, 900 copies were downloaded in the first 24 hours. By the end of...
Problem 3 Assume that the probability of rain tomorrow is 0.5 if it is raining today,...
Problem 3 Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today. a) Find the n-step transition matrix for n = 3, 7, 10, 20. b) The probability of rain today is 0.5 Use the results in the part...
The impact of inventory increases on the business cycle depends upon whether [the increases] are planned...
The impact of inventory increases on the business cycle depends upon whether [the increases] are planned or unplanned.  Do you agree?  Briefly explain.
Suppose that whether or not it rains today depends on previous weather conditions through the last...
Suppose that whether or not it rains today depends on previous weather conditions through the last two days. Specifically, suppose that if it has rained for the past two days, then it will rain tomorrow with probability 0:7; if it rained today but not yesterday, then it will rain tomorrow with probability 0:5; if it rained yesterday but not today, then it will rain tomorrow with probability 0:4; if it has not rained in the past two days, then it...
Suppose that whether or not it rains today depends on previous weather conditions through the last...
Suppose that whether or not it rains today depends on previous weather conditions through the last two days. Specifically, suppose that if it has rained for the past two days, then it will rain tomorrow with probability 0.7; if it rained today but not yesterday, then it will rain tomorrow with probability 0.5; if it rained yesterday but not today, then it will rain tomorrow with probability 0.4; if it has not rained in the past two days, then it...
Under which situations Earnings Per share goes up and stock price goes down ?
Under which situations Earnings Per share goes up and stock price goes down ?
“If a stock goes up, you should sell it to lock in the gain and buy...
“If a stock goes up, you should sell it to lock in the gain and buy another stock, but if it goes down you should hold it to recoup the loss”. Evaluate this statement a) with no taxes, and b) with taxes.
Question 1 (1 point) Samsung’s stock price goes up 30% but the Korean won falls 20%...
Question 1 (1 point) Samsung’s stock price goes up 30% but the Korean won falls 20% against the Japanese yen. From the perspective of a Japanese investor, what is the yen return on an investment in Korea’s Samsung? [Hint: Assume that Ptd = Ptf Std/f, where, Ptd = domestic price; Ptf = foreign price and Std/f = spot price; return from asset price: (1+rd) = (Ptd/Pt-1d) and return from FX spot price: (1+sd/f) = (Std/f/St-1d/f)]. Question 1 options: a) loss...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT