Problem 4. Consider the following dynamics. If today is sunny, tomorrow will be sunny with aprobability of 0.5, cloudy with a probability of 0.4 and rainy with a probability of 0.1. If today iscloudy, tomorrow will be sunny, cloudy, or rainy, with a probability of 0.5, 0.2, and 0.3,respectively. Lastly, if today is rainy, tomorrow will be sunny, cloudy, or rainy with a probabilityof 0.7, 0.2, and 0.1, respectively.a) Draw the corresponding Markov Chain. Clearly define your state space, draw the states andtransitions, and include the probabilities on each arc.b) Starting on a Sunny day, what is the mean first passage time till a Rainy day.c) Starting on a rainy day, what is the mean recurrence time.

Answered: Image /qna-images/answer/9b03abb6-c5a7-476e-9a6f-0b808764f7a5.jpg

Answered: Problem 4. Consider the following…

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...

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Suppose that 75% of science students, 45% of business students, and 45% of humanities students pass a mathematics course. If 15% of the students in the course are science students, 15% are business students and 70% are humanities students, then the probability that a randomly selected student who has passed the course is a science student is O a. 0.429 O b. 0.214 O c. 0.525 d. 0.357 O e. 0.643
(i) If volume is high this week, then next week it will be high with a probability of 0.9 and low with a probability of 0.1.(ii) If volume is low this week then it will be high next week with a probability of 0.5.Assume that state 1 is high volume and that state 2 is low volume. 1. If the volume this week is high, what is the probability that the volume will be high two weeks from now? 2. What is the probability that volume will be high for three consecutive weeks?
A store specializing in mountain bikes is to open in one of two malls. If the first mall is selected, the store anticipates a yearly profit of $1,425,000 if successful and a yearly loss of $475,000 otherwise. The probability of success is 1. If the second mall is selected, it is estimated that the yearly profit will be $950,000 if successful; 3 otherwise, the annual loss will be $285,000. The probability of success at the second mall is Complete parts (a) through (c) below 4 - a. What is the expected profit for the first mall?
Problem 1. A certain disease has a prevalence of one in every 100 individuals in the population. A test for this disease has a false positive rate of 10% and a false negative rate of 3%. The rate of false positives and false negatives depends only on whether or not the tested individual has the disease. What is the probability that an individual who tests positive twice for the disease has the disease? What is the probability that an individual who tests negative twice for the disease has the disease?
Solve the following probabilty problem: Doris and her friend plan to travel to Florida during the winter intersession period. Based upon the past experience they know that the probability that they go by car is 0.4 and the probability that they go by plane is 0.2. What is the probability that they travel to Florida by car or plane only?
Suppose an oil company is thinking of buying some land for $10,000,000. There is a 60%60% chance of economic growth and a 40%40% chance of recession. The probability of discovering oil is 44%44% when there is economic growth and 32%32% when there is a recession. If there is economic growth and the oil company discovers oil, the value of the land will triple. If they do not discover oil, the value of the land will decrease by 10%.10%. If there is a recession and the company discovers oil, the value of the land will increase by 50%.50%. If they do not discover oil, the land will decrease in value by 75%.75%. What is the expected value of the investment? Give your answer to the nearest dollar. Avoid rounding within calculations. $$ Select the correct interpretation of the expected value. The expected value represents what the actual investment value will be for this land purchase of $10,000,000. The company should make the investment because the expected value…
Problem 2 [12 points]: Fourth digit of ID a. Genuine motor company manufactures an assembly which consists of three mechanical components. Suppose that the probability of not meeting specification for the first component is equal to 0.09/ 0.11/ 0.13. For the second and third components the probabilities of not meeting specifications are 0.05/ 0.04/ 0.03 and 0.06/ 0.07/ 0.08 respectively. Assuming that the components are independent in terms of not meeting the specification, determine the probability mass function of the number of components in the assembly that does not meet specification. (6.0) Fifth digit of ID Last digit of ID
Problem (2): TV or a DVR? A consumer electronics company has observed that 36% of their customers purchased an LED screen television, 26% of their customers purchases a DVR, and 12 percent of their customers purchased both an LED screen TV and a DVR. Find the probability that a randomly chosen customer either purchases a plasma screen TV or a DVR.
Problems #4: At a certain steakhouse, the probability a customer purchases a chicken dinner is 0.48 and the probability a customer purchases a side-salad is 0.41. The probability a customer purchases only a side-salad and not a chicken dinner is 0.05. a. What is the probability a customer purchases both a chicken dinner and a side salad? b. If a customer purchases the chicken dinner, what is the probability s/he does not purchase the side-salad? c. What is the probability the customer purchases neither the chicken dinner, nor the side-salad? d. What is the probability the customer purchases one of the 2 options, but not both? e. Suppose 2 customers come in to the restaurant (in different parties). What is the probability both of them purchase the chicken dinner and side-salad?

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