Data have been accumulated on the heights of children relative to their parents. Suppose that the probabilities that a tall parent will have a tall, medium-height, or short child are 0.5, 0.3, and 0.2, respectively; the probabilities that a medium-height parent will have a tall, medium-height, or short child are 0.2, 0.6, and 0.2, respectively; and the probabilities that a short parentwill have a tall, medium-height, or short child are 0.2, 0.3, and 0.5, respectively.(a) Write down the transition matrix for this Markov chain. (Order rows by tall first, medium second, and short third.).5.3.226.2.23.5(b) What is the probability that a short person will have a tall grandchild?X(c) If 30% of the current population is tall, 30% is of medium height, and 40% is short, what will the distribution be in three generations?(d) What proportion of the population will be tall, of medium height, and short in the long run?

As per guidelines,we are supposed to solve first 3 subparts only.

Answered: Data have been accumulated on the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A manufacturing company is faced with the problems of choosing four products to manufacture. The potential demand for each product may turn out to be good, satisfactory, or poor. Probabilities for each type are given below: Products Probabilities Good Satisfactory Рoor A 0.60 0.20 0.20 В 0.75 0.15 0.10 C 0.60 0.25 0.15 D 0.50 0.20 0.30 The estimated profit/loss under different states of demand may be taken as under. uct Profit or Loss Good Satisfactory Poor A 40,000 10,000 1,100 40,000 20,000 |-7,000 C 50,000 15,000 |-8,000 D 40,000 18,000 15,000 Prepare expected value table and advice the company about the choice of the product.
A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (22)%, and (13)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2?
A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (20+I)%, and (10+H)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2? H is 3 and I is 2
The proprietor of Midland Construction Company has to decide between two projects. He estimates that the first project will yield a profit of $160,000 with a probability of 0.7 or a profit of $120,000 with a probability of 0.3; the second project will yield a profit of $220,000 with a probability of 0.6 or a profit of $70,000 with a probability of 0.4.Find the expected profit for each project. first project $ second project $ Which project should the proprietor choose if he wants to maximize his expected profit? first project second project
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Find P(A or B or C) for the given probabilities. P(A) = 0.34, P(B) = 0.25, P(C) = 0.16 P(A and B) = 0.11, P(A and C) = 0.03, P(B and C) = 0.07 P(A and B and C) = 0.01 P(A or B or C) =
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At the beginning of each day, a patient in the hospital is classifed into one of the three conditions: good, fair or critical. At the beginning of the next day, the patient will either still be in the hospital and be in good, fair or critical condition or will be discharged in one of three conditions: improved, unimproved, or dead. The transistion probabilities for this situation are Good Fair Critical Good 0.65 0.20 0.05 Fair 0.50 0.30 0.12 Critical 0.51 0.25 0.20 Improved Unimproved Dead Good 0.06 0.03 0.01 Fair 0.03 0.02 0.03 Critical 0.01 0.01 0.02 For example a patient who begins the day in fair condition has a 12% chance of being in critical condition the next day and a 3%…
John is having a dinner at a restaurant, which sells 3 kinds of dishes, A, B, and C. The probabilities of ordering each dish are 0.4, 0.3, and 0.3. Suppose the probability of John being satisfied after eating the dishes are 0.7, 0.5, and 0.6, respectively. Answer the questions below. 1) When John wasn’t satisfied with his dish, what is the probability that he has eaten the dish B? (Round an answer to two decimal places.) 2) What is the probability that John satisfies after eating the dish?
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A gas station has three grades of fuel, regular, premium and diesel. Due to problems with the supply chain, the probabilities that the station will run out of any three fuel types in a week are 0.10, 0.16 and 0.24, respectively. These probabilities are statistically independent. Also, if there is a shortage of diesel, the probability of a shortage of premium becomes 0.25. 1. How likely is the station to run out of all three fuels in a given week? 2. What is the probability that if regular runs out, both premium and diesel will also run out? 3. What is the probability that the station will run out of at least one of either premium and diesel? 4. What is the probability that the station will run out of at least 2 of the fuels in a week?

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