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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Problem 1. In a weekday, Jeremy will eat panda express 35% of the time, drink Starbucks 40% of the time. And if given he doesn't drink Starbucks, the probability he eats panda express is .5. Calculate the probability he will eats panda express and drink Starbucks at the same time.
Problem 1) From previously published studies, the probability that a pine snake hatched in a zoo will survive to maturity is 72%. If five pine snakes are hatched, what is the predicted probability distribution for the number of pine snakes that will survive to maturity? (Find Prob(X=k) for k = 0, 1, 2, 3, 4, and 5.) Carry three decimal places in your calculations. 1. Choose the correct answer for k = 0 а. 0.022 b. 0.020 с. 0.002 d. 0.030 2. Choose the correct answer for k= 1 а. 0.022 b. 0.020 с. 0.002 d. 0.030
(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?
Question 2: For a certain airline, there is a 75% probability that a given flight will depart on-time, an 80% probability of an on-time arrival, and a 60% probability of both an on-time departure and arrival. What is the probability that this flight will either depart on-time or arrive on-time? Is on-time arrival independent of on-time departure?
Please answer question below
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?
Question 1 According to the Chronicles of Contrived Statistics (March, 2016), the probability that scientists from Area 51 will begin selling pet aliens in the next month is 20%. The probability that either Elon Musk will offer you a free trip to space or that scientists will begin sales of pet aliens next month is 43%. Finally, they list that probability of both happening in the next month is 13%. What is the probability that Elon Musk will offer you a free trip into space in the next month? Round to two decimal places as needed.
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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