Assuming that the climate in the city of Metepec behaves according to a Markov chain, consider the following data. The probability of rain on any following day is 70% if it rained the day before, and 20% if it did not rain the day before; Likewise, the probability that the next day will be dry is 80% if the day before was dry, and 30% if it rained the day before. From this information: C. Find the probability that Friday is a dry day, given that it rained today, Tuesday. D. Suppose you want to calculate the probability that it will rain in exactly six months, describe two different strategies you could use to perform this calculation. Would it really matter to consider what the weather was today?

Assuming that the climate in the city of Metepec behaves according to a Markov chain, consider the following data. The probability of rain on any following day is 70% if it rained the day before, and 20% if it did not rain the day before; Likewise, the probability that the next day will be dry is 80% if the day before was dry, and 30% if it rained the day before. From this information: C. Find the probability that Friday is a dry day, given that it rained today, Tuesday. D. Suppose you want to calculate the probability that it will rain in exactly six months, describe two different strategies you could use to perform this calculation. Would it really matter to consider what the weather was today?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: It costs $10 to play a gambling game. If the player wins, then this $10 is returned and an…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Central topic markov chains: Young Filibonio (who likes steak), Petronilo (who likes chicken) and…

Q: UInities given in the fo. B 0.14 0,15

Q: Suppose we play Rock-Paper-Scissors with the strategy of throwing rock, paper, or scissors randomly…

A: Given the transition matrix as R P SP=RPS0132312012100

Q: Consider four wireless operators A, S, T, and V in a major metropolitan area. Suppose each of them…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: What is the probability that all three components function properly throughout the warranty period?…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Q: Suppose a room has two lamps, but to have adequate light both lamps must work (success) when turned…

A: Given data: P1 = P(First lamp working) = 0.98 P2 = P ( second lamp working ) = 0.85 To find: The…

Q: You witnessed the following sequence of outcomes from an experiment (where each individual letter is…

Q: In Manhattan during spring the weather was quite strange of its has both sunny and rainy days and…

A: Given A sunny day is followed by a sunny day with probability 0.8 and A rainy day is by a rainy…

Q: The following system operates only if there is a path of functional devices from the leftmost entry…

Q: Here is the Markov Chain (enclosed), then… ▪ Which state are communicating? ▪ Which are the…

Q: Suppose that 100 students take a test in a class. Each student has a 2/3 probability of passing the…

A: a. Markov's Inequality:Markov's Inequality states that for a non-negative random variable X and any…

Q: Consider two different states i and j of a Markov chain. Which of the following choices can NEVER be…

A: The probability of going from state i to state j in exactly 3 steps is strictly less than the first…

Q: 3. Real Cheap Car Rental Agency operates agencies in two cities, city 1 and city 2. The fractions of…

Q: The weather in the Magical Land of Oz only depends on the weather from the previous day. There are…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: vertising to swite rs "unyielding" probabilities gi

Q: A mouse is placed in room 3 of the maze shown to the right. At each step the mouse exits the…

Q: a.Here is the Markov Chain, then : Which state is communicating? Which are the transient states? The…

A: Given the transition diagram of the Markov chain:

Q: Are events Q and S independent events?

A: ALASKA INVESTMENT CORP has decided to choose two of a group of three utility stocks. Suppose we…

Q: ALASKA INVESTMENT CORP has decided to choose two of a group of three utility stocks. Suppose we…

Q: Given the Markov Chain (S, ro, P) where S = {$1, 82, 83}, To , and [o 3 .21 Г.3 .14 P = |1 0 .4 p² =…

Q: The following Markov matrix describes a stochastic process involving 3 states 81, 82, 83. The number…

A: As per our guideline we can solve only first four subparts. Please repost for another questions.…

Q: 6. A Markov chain has two non-absorbing states, A and B, and two absorbing states, C and D. Below…

A: Given information: The transition probabilities are, P(A to A)=10%=0.10 P(A to B)=20%=0.20 P(A to…

Q: Consider the following Markov chain. Assuming that the process starts in state 3, what is the…

A: Given the transition diagram of a Markov chain with 6 states as

Q: Draw the transition probability graph and construct the transition probability matrix of the…

Q: A system consists of four components which are working independently. A has a reliability of 90%…

A: Given that: PA=PB=0.9PC=PD=0.8 a) Now, the system works if both A and B work and either of C or D…

Q: Fifty-four players participated in the 1980 World Series of Poker. Each player began with $10,000.…

A: A poker game cannot be called a Markov chain, because this game is not dependent exclusively on the…

Q: 0.7 031 0.4 0.6 0.5 0.5 0.5 0.1. lo.4 States are 0,1,2,3 respectively. a. Does this Markov chain…

Q: Fifty-four players (including Gabe Kaplan and JamesGarner) participated in the 1980 World Series of…

A: To model the World Series of Poker as a Markov chain, we need to define the states and transitions…

Q: There is a 0.45 probability that the Morgan company (a paper manufacturer) will send a sales rep. to…

A: Let 'X' be the event represents that the Morgan company will send a sales representative. And, 'X'…

Q: 3. Construct a model of population flows between cities, suburbs, and nonmetropolitan areas of the…

Q: 0.9 0.4 0.1 တ လ 1 2 0.6 0.2 0.4 3 0.2 0.7 5 2 0.2 0.3 1 6

A: There are following ways to go to recurrent class { 2,3} 1. State 4 to 3, state 3 to state 2 2.…

Q: The following data consists of a matrix of transition probabilities (P) of three competing…

Q: The elevator of a building with a ground floor and two floors makes trips from one floor to another.…

A: Given that an elevator of a building with a ground floor and two floors makes trips from one floor…

Question

C. Find the probability that Friday is a dry day, given that it rained today, Tuesday.

D. Suppose you want to calculate the probability that it will rain in exactly six months, describe two different strategies you could use to perform this calculation. Would it really matter to consider what the weather was today?

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Markov Processes and Markov chain$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Consider the Markov chain specified by the following transition diagram. a. Find the steady-state probabilities of all states. 0.4 b. If the initial state is 7, what is the expected 0.3 0.4 0.2 number of steps to reach state 1 or 3? 0.8 0.2 c. If at step 0 the system was in state 4, what is the probability that after step 3 it was in state 3 and after step 47 it was in state 3 again?
Question 1.16.2 (Markov chains, Part IB, 1991, 307D) Three girls A, B and C are playing table tennis. In each game, two of the girls play against each other and the third girl does not play. The winner of any given game n plays again in game n + 1. The probability that girl x will beat girl y in any game that they play against each other is sx/(Sx+Sy) for x, y = {A,B,C}, x‡y, where sa, SB, SC represent the playing strengths of the three girls. In what proportion of games does each girl play, in the long run?
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. 0.4 2300 T 0.3 2800 0.2 2500 2400 From/To A B C D A 0.2 0 0.3 0.3 B 0.3 0.2 0.5 0.4 C 0.1 0.5 0 0.3 D 0 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. c) What is the mean return time of Brand A? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? Number of Customers d) What is the percentage change of Brand B? Answer in percentage and in 2 decimal places.
3. Consider an undiscounted Markov decision process with three states 1, 2, 3, with respec- tive rewards -1, -2,0 for each visit to that state. In states 1 and 2, there are two possible actions: a and b. The transitions are as follows: • In state 1, action a moves the agent to state 2 with probability 0.8 and makes the agent stay put with probability 0.2. In state 2, action a moves the agent to state 1 with probability 0.8 and makes the agent stay put with probability 0.2. . In either state 1 or state 2, action b moves the agent to state 3 with probability 0.1 and makes the agent stay put with probability 0.9. Find the optimal policy that minimises the expected total cost and find the corresponding value function.
The following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 2 after two periods is a. 0.283 b. 0.26 c. 0.261 d. 0.47
Hw 4 The following information relates to the probability of two different managers selecting a salesperson for a job: Probability of Manager Sam choosing a Salesperson is 0.5 Probability of Manager Alex choosing a Salesperson is 0.3 Over the last 10 working days, Manager Sam has worked for 6 days and Manager Alex worked 4 days. Only one manager works in a day. Required: Build a Tree diagram to show the probabilities of a Salesperson being selected. Show the different branches of the Tree diagram with all the calculations. Include in the Tree diagram the overall probabilities.
Please do the following questions with handwritten working out. Answer is in other image
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?
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A₁ be the event that the receiver functions properly throughout the warranty period, A₂ be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A₁) = 0.92, P(A₂) = 0.96, and P(A3) = 0.90. (Round your answers to four decimal places.) (a) What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period? (d) What is the probability that only the receiver needs service during the warranty period? (e) What is the probability that exactly one of the three components needs service…
In any given day the air quality in a certain city is either good or bad. Records show that when the air quality is good on one day, then there is a 95% chance that it will be good the next day, and when the air quality is bad on one day, then there is 45% chance it will be bad the next day. a. Give the transition matrix. b. if the air quality is good today, what is the probability it will be good two days from now? c. if the air quality is bad today, what is the probability it will be bad three days from now? d. if the there is 20% chance the air quality is good today, what is the probability it will be good tomorrow?
Given the following Markov Chain diagram. 0.15 On Duty Off 0.85 0.2 Duty 0.8 Given that you were on duty the first day (i.e., P(Day 1=On Duty) = 1 and P(Day %3D 1= Off Duty) = 0), answer the following questions. • What is the probability that you need to report towork on the 2mnd day (i.e., P(Day 2 = On Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you take a leave on the 2nd day (i.e., P(Day 2 = Off Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you go to work on the third day (i.e., P(Day 3=On Duty))? Answer: |(Please write your answer with 4 decimal points) • What is the probability that the third day was a Day Off (i.e., P(Day 3=Day Off)? Answer: (Please write your answer with 4 decimal points)