You witnessed the following sequence of outcomes from an experiment (where each individualletter is a single piece of data): A AABABBAABAAABBAABABBAAA Draw a picture of a2nd order Markov chain representing this data set. You can express all probabilities as fractions (noneed to convert to decimals), though you should simplify where possible (e.g. convert 5/10 to 1/2).Next, you want to use the Markov chain that you have drawn to make some predictions based on anew set of test data. The test data is as follows: A BABAA Based on the model that you drew, whatis the probability that the next outcome after the above sequence of test data is B? You can expressyour answer as a fraction. Now, imagine that your prediction was correct, and the next outcome wasB. Given this new outcome and the prior sequence of test data, what is the probability that the nextoutcome after the new outcome (which you just witnessed to be B) is A?

Answered: Image /qna-images/answer/25937df4-13e4-468a-9704-ee08c6822193.jpg

Answered: You witnessed the following sequence of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A firm making production plans believes there is a 30% probability the price will be $10, a 50% probability the price will be $15, and a 20% probability the price will be $20. The manager must decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The following table shows 9 possible outcomes depending on the output chosen and the actual price. Production Profit (Loss) when price is $10 $15 $20 6,000 (A) −$200 $400 $1,000 8,000 (B) −$400 $600 $1,600 10,000 (C) −$1,000 $800 $3,000 What is the variance if 6,000 units are produced?
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 7% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month?
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B where only ( )%? stay with them and ( )%? switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B?1=? MDA?2=?
Draw an appropriate tree diagram, and use the multiplication principle to calculate the probabilities of all the outcomes. HINT [See Example 3.] It appears that there is only a one in four chance that you will be able to take your spring vacation to the Greek Islands. If you are lucky enough to go, you will visit either Corfu (30% chance) or Rhodes. On Rhodes there is a 40% chance of meeting a tall, dark stranger, while on Corfu there is no such chance. P(Go to Corfu and meet a tall, dark stranger) P(Go to Corfu and meet no tall, dark stranger) P(Go to Rhodes and meet a tall, dark stranger) P(Go to Rhodes and meet no tall, dark stranger) P(No vacation) = = || || || || =
In a population of 10,000, there are 5000 nonsmokers, 2500 smokers of one pack or less per day, and 2500 smokers of more than one pack per day. During any month, there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 9% probability of quitting and a 10% probability of dropping to a pack or less per day. How many people will be in each group in 1 month, in 2 months, and in 1 year? (Round your answers to the nearest whole number.)(a) in 1 month:nonsmokers:1 pack/day or less:more than 1 pack/day:(b) in 2 months:nonsmokers:1 pack/day or less:more than 1 pack/day:(c) in 1 year:nonsmokers:1 pack/day or less:more than 1 pack/day:
The weather in Columbus is either good, indifferent, or bad on any given day. If the weather is good today, there is a 40% chance it will be good tomorrow, a 30% chance it will be indifferent, and a 30% chance it will be bad. If the weather is indifferent today, there is a 50% chance it will be good tomorrow, and a 20% chance it will be indifferent. Finally, if the weather is bad today, there is a 10% chance it will be good tomorrow and a 30% chance it will be indifferent. a. What is the stochastic matrix, P, for this situation? b. Suppose there is a 10% chance of good weather today and a 90% chance of indifferent weather. What are the chances of bad weather tomorrow? c. Suppose the predicted weather for Monday is 40% indifferent weather and 60% bad weather. What are the chances for good weather on Wednesday? a. Create the stochastic matrix, P, where G is good, I is indifferent, and B is Bad. From: GIB a (Simplify your answers.) To: G
In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly diagnosis 95% of all persons with diabetes as having the disease and incorrectly diagnoses ten percent of all persons without diabetes as having the disease, find the probabilities that: The health service will diagnose an adult over age 50 as having diabetes. A person over 50 diagnosed by the health service as having diabetes actually has the disease.
ne bets $1. 0.45, he wins the game and with probability 1 - p = 0.55, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? • What is the probability that he goes broke?
From a large survey of customers using a chain of coffee shops, 60% of the customers are male, 50% purchase food, 15% are both Male and purchase food. What are the probabilities that: A customer is both female and purchases food? A female customer purchases food? A customer purchasing food is female?
A trader invented a strategy where he can either win or lose a certain amount of money every day (say, k dollars) with equal probability, independently of all other days. (In fact, such a strategy is not very difficult to implement - buy a very liquid asset whose price moves without major jumps and liquidate the position as soon as you are making or losing k dollars). He then made the following statement: “If I use my strategy every day for the next 400 days, my chances of staying within 10,000 dollars of the original account balance are equal to 1/3.(a) What is k (approximately)?(b) What are his chances (approximately) of making over 20,000 with this strategy in 400 days?
In the city of Savannah, Georgia, 22% of young couples take wedding pictures along the Riverwalk (R), and 42% of young couples take wedding pictures in one of the many historical squares (S) throughout the city. However, only 14% of young couples take wedding pictures along the Riverwalk and in the squares. Are these two events independent of each other? Include the reason why or why not. A. The events aren't independent, because P(R) × P(S) ≠ P(P and S). B. The events are independent, because P(R) × P(S) ≠ P(P and S). C. The events aren't independent, because P(R) × P(S) = P(P and S). D. The events are independent, because P(R) × P(S) = P(P and S)
Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), standard (cage with other rats), enriched (cage with other rats and toys), super enriched (cage with rats and toys changes on a periodic basis). After two months, the rats were tested on a variety of learning measures (including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure (overall cortical weight, degree of dendritic branching, etc.). The data for the maze task is below. Compute the appropriate test for the data provided below. Include solution. Thank you

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