Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 2.1, Problem 15P
Program Plan Intro
Program Description: Purpose of the problem is to prove that the limiting population is
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Generate 100 synthetic data points (x,y) as follows: x is uniform over [0,1]10 and y = P10 i=1 i ∗ xi + 0.1 ∗ N(0,1) where N(0,1) is the standard normal distribution. Implement full gradient descent and stochastic gradient descent, and test them on linear regression over the synthetic data points.
Subject: Python Programming
Computer Science
Consider the demand and supply system
p = ad +bdqd +ud
p = as +bsqs +us
with the equilibrium condition qd = qs = q. The parameters bd and bs are −2 and 1.5, respectively. Find the parameters ad and as are such that q = 5 and p = 10.
Throughout this question use N = 100, and set the random seed to 14022022. The variable ud has a standard deviation of 3. All randomly generated variables have a mean of zero and are normally distributed unless something else is specified. All Monte Carlo studies should be done with 10,000 repetitions.
Part a. Illustrate the supply and demand curves in a graph, together with a sample of simulated price and quantity data. Provide an additional graph where you have included the OLS estimated line of demand equation above. Are your estimates close to the true values of ad and bd ?
Solve the question in Python language on Jupyter notebook.
Solve in R programming language:
Suppose that the number of years that a used car will run before a major breakdown is exponentially distributed with an average of 0.25 major breakdowns per year.
(a) If you buy a used car today, what is the probability that it will not have experienced a major breakdown after 4 years.
(b) How long must a used car run before a major breakdown if it is in the top 25% of used cars with respect to breakdown time.
Chapter 2 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.1 - Prob. 5PCh. 2.1 - Prob. 6PCh. 2.1 - Prob. 7PCh. 2.1 - Prob. 8PCh. 2.1 - Prob. 9PCh. 2.1 - Prob. 10P
Ch. 2.1 - Prob. 11PCh. 2.1 - Prob. 12PCh. 2.1 - Prob. 13PCh. 2.1 - Prob. 14PCh. 2.1 - Prob. 15PCh. 2.1 - Prob. 16PCh. 2.1 - Prob. 17PCh. 2.1 - Prob. 18PCh. 2.1 - Prob. 19PCh. 2.1 - Prob. 20PCh. 2.1 - Prob. 21PCh. 2.1 - Suppose that at time t=0, half of a logistic...Ch. 2.1 - Prob. 23PCh. 2.1 - Prob. 24PCh. 2.1 - Prob. 25PCh. 2.1 - Prob. 26PCh. 2.1 - Prob. 27PCh. 2.1 - Prob. 28PCh. 2.1 - Prob. 29PCh. 2.1 - A tumor may be regarded as a population of...Ch. 2.1 - Prob. 31PCh. 2.1 - Prob. 32PCh. 2.1 - Prob. 33PCh. 2.1 - Prob. 34PCh. 2.1 - Prob. 35PCh. 2.1 - Prob. 36PCh. 2.1 - Prob. 37PCh. 2.1 - Fit the logistic equation to the actual U.S....Ch. 2.1 - Prob. 39PCh. 2.2 - Prob. 1PCh. 2.2 - Prob. 2PCh. 2.2 - Prob. 3PCh. 2.2 - Prob. 4PCh. 2.2 - Prob. 5PCh. 2.2 - Prob. 6PCh. 2.2 - Prob. 7PCh. 2.2 - Prob. 8PCh. 2.2 - Prob. 9PCh. 2.2 - Prob. 10PCh. 2.2 - Prob. 11PCh. 2.2 - Prob. 12PCh. 2.2 - Prob. 13PCh. 2.2 - Prob. 14PCh. 2.2 - Prob. 15PCh. 2.2 - Prob. 16PCh. 2.2 - Prob. 17PCh. 2.2 - Prob. 18PCh. 2.2 - Prob. 19PCh. 2.2 - Prob. 20PCh. 2.2 - Prob. 21PCh. 2.2 - Prob. 22PCh. 2.2 - Prob. 23PCh. 2.2 - Prob. 24PCh. 2.2 - Use the alternatives forms...Ch. 2.2 - Prob. 26PCh. 2.2 - Prob. 27PCh. 2.2 - Prob. 28PCh. 2.2 - Consider the two differentiable equation...Ch. 2.3 - The acceleration of a Maserati is proportional to...Ch. 2.3 - Prob. 2PCh. 2.3 - Prob. 3PCh. 2.3 - Prob. 4PCh. 2.3 - Prob. 5PCh. 2.3 - Prob. 6PCh. 2.3 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - A motorboat weighs 32,000 lb and its motor...Ch. 2.3 - A woman bails out of an airplane at an altitude of...Ch. 2.3 - According to a newspaper account, a paratrooper...Ch. 2.3 - Prob. 12PCh. 2.3 - Prob. 13PCh. 2.3 - Prob. 14PCh. 2.3 - Prob. 15PCh. 2.3 - Prob. 16PCh. 2.3 - Prob. 17PCh. 2.3 - Prob. 18PCh. 2.3 - Prob. 19PCh. 2.3 - Prob. 20PCh. 2.3 - Prob. 21PCh. 2.3 - Suppose that =0.075 (in fps units, with g=32ft/s2...Ch. 2.3 - Prob. 23PCh. 2.3 - The mass of the sun is 329,320 times that of the...Ch. 2.3 - Prob. 25PCh. 2.3 - Suppose that you are stranded—your rocket engine...Ch. 2.3 - Prob. 27PCh. 2.3 - (a) Suppose that a body is dropped (0=0) from a...Ch. 2.3 - Prob. 29PCh. 2.3 - Prob. 30PCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.4 - Prob. 10PCh. 2.4 - Prob. 11PCh. 2.4 - Prob. 12PCh. 2.4 - Prob. 13PCh. 2.4 - Prob. 14PCh. 2.4 - Prob. 15PCh. 2.4 - Prob. 16PCh. 2.4 - Prob. 17PCh. 2.4 - Prob. 18PCh. 2.4 - Prob. 19PCh. 2.4 - Prob. 20PCh. 2.4 - Prob. 21PCh. 2.4 - Prob. 22PCh. 2.4 - Prob. 23PCh. 2.4 - Prob. 24PCh. 2.4 - Prob. 25PCh. 2.4 - Prob. 26PCh. 2.4 - Prob. 27PCh. 2.4 - Prob. 28PCh. 2.4 - Prob. 29PCh. 2.4 - Prob. 30PCh. 2.4 - Prob. 31PCh. 2.5 - Prob. 1PCh. 2.5 - Prob. 2PCh. 2.5 - Prob. 3PCh. 2.5 - Prob. 4PCh. 2.5 - Prob. 5PCh. 2.5 - Prob. 6PCh. 2.5 - Prob. 7PCh. 2.5 - Prob. 8PCh. 2.5 - Prob. 9PCh. 2.5 - Prob. 10PCh. 2.5 - Prob. 11PCh. 2.5 - Prob. 12PCh. 2.5 - Prob. 13PCh. 2.5 - Prob. 14PCh. 2.5 - Prob. 15PCh. 2.5 - Prob. 16PCh. 2.5 - Prob. 17PCh. 2.5 - Prob. 18PCh. 2.5 - Prob. 19PCh. 2.5 - Prob. 20PCh. 2.5 - Prob. 21PCh. 2.5 - Prob. 22PCh. 2.5 - Prob. 23PCh. 2.5 - Prob. 24PCh. 2.5 - Prob. 25PCh. 2.5 - Prob. 26PCh. 2.5 - Prob. 27PCh. 2.5 - Prob. 28PCh. 2.5 - Prob. 29PCh. 2.5 - Prob. 30PCh. 2.6 - Prob. 1PCh. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Prob. 4PCh. 2.6 - Prob. 5PCh. 2.6 - Prob. 6PCh. 2.6 - Prob. 7PCh. 2.6 - Prob. 8PCh. 2.6 - Prob. 9PCh. 2.6 - Prob. 10PCh. 2.6 - Prob. 11PCh. 2.6 - Prob. 12PCh. 2.6 - Prob. 13PCh. 2.6 - Prob. 14PCh. 2.6 - Prob. 15PCh. 2.6 - Prob. 16PCh. 2.6 - Prob. 17PCh. 2.6 - Prob. 18PCh. 2.6 - Prob. 19PCh. 2.6 - Prob. 20PCh. 2.6 - Prob. 21PCh. 2.6 - Prob. 22PCh. 2.6 - Prob. 23PCh. 2.6 - Prob. 24PCh. 2.6 - Prob. 25PCh. 2.6 - Prob. 26PCh. 2.6 - Prob. 27PCh. 2.6 - Prob. 28PCh. 2.6 - Prob. 29PCh. 2.6 - Prob. 30P
Knowledge Booster
Similar questions
- (Do it on R)(using Pnorm) The loaves of rye bread distributed to local stores by a certain bakery have an average length of 30 centimeters and a standard deviation of 2 centimeters. Assuming that the lengths are normally distributed, what percentage of the loaves are (a) longer than 31.7 centimeters? (b) between 29.3 and 33.5 centimeters in length? (c) shorter than 25.5 centimeters?arrow_forward2. Given a Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9}, and Event B = {3, 7, 9, 11, 12, 13} Find the probability P(A|B). State your answer as a value with one digit after the decimal point.arrow_forwardIn a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet.arrow_forward
- In a lake, the population of a particular fish species is about 1 million. Fish reproduce by 20% of the population each month, regardless of the season. In addition, fish die naturally after living for an average of 10 months. There are two separate companies (for example, A and B) fishing with 5 boats on the edge of this lake. According to current data, each boat catches 5000 fish per month. However, if the total number of boats caught in the lake increases, the number of fish to be caught by each boat decreases, as the boats will prevent each other from fishing. In addition, if the fish population in the lake increases, the fish caught per boat increases, and if the population decreases, the fish caught per boat decreases. As companies earn money from hunting, they want to buy new boats over time and enlarge their boat fleet. Indicate the causal relationships in this system with arrows and signs. Show the causality loops in this system, at least 1 negative, at least 1 positive, and…arrow_forwardWhen a temperature gauge surpasses a threshold, your local nuclear power station sounds an alarm. Core temperature is gauged. Consider the Boolean variables A (alarm sounds), FA (faulty alarm), and FG (faulty gauge) and the multivalued nodes G (gauge reading) and T (real core temperature). Since the gauge is more likely to fail at high core temperatures, draw a Bayesian network for this domain.arrow_forwardA seller has an indivisible asset to sell. Her reservation value for the asset is s, which she knows privately. A potential buyer thinks that the assetís value to him is b, which he privately knows. Assume that s and b are independently and uniformly drawn from [0, 1]. If the seller sells the asset to the buyer for a price of p, the seller's payoff is p-s and the buyer's payoffis b-p. Suppose simultaneously the buyer makes an offer p1 and the seller makes an offer p2. A transaction occurs if p1>=p2, and the transaction price is 1/2 (p1 + p2). Suppose the buyer uses a strategy p1(b) = 1/12 + (2/3)b and the seller uses a strategy p2(s) = 1/4 + (2/3)s. Suppose the buyer's value is 3/4 and the seller's valuation is 1/4. Will there be a transaction? Explain. Is this strategy profile a Bayesian Nash equilibrium? Explain.arrow_forward
- it is known that a natural. law obeys the quadratic relationship y=ax^2.what is the best line of form y=px+q that can be used to model data and minimise Mean-squared-error, if all of the data points are drawn uniformly at random from the domain [0,1]?arrow_forwardMatch the following sentence to the best suitable answer: - A. B. C. D. for the linear congruence ax=1(mod m), x is the inverse of a, if__________ - A. B. C. D. What is -4 mod 9 ? - A. B. C. D. The solution exists for a congruence ax=b(mod m) such that GCD(a,m)=1 and - A. B. C. D. (107+22)mod 10 is equivalent to :_________ A. 5 B. c divides b C. GCD(a,m)=1 D. 9 mod 10arrow_forwardConsider a system with input x(t) and output y(t) . The relationship between input and output is y(t) = x(t)x(t − 2) a. Is the system causal or non-causal?b. Determine the output of system when input is Aδ(t) , where A is any real orcomplex number?arrow_forward
- Given a two-category classification problem under the univariate case, where there are two training sets (one for each category) as follows: D₁ = (-3,-1,0,4} D₂ = {-2,1,2,3,6,8} Given the test example x = 5, please answer the following questions: have and a) Assume that the likelihood function of each category has certain paramétric form. Specifically, we p(x | w₁) N, 07) p(x₂)~ N(μ₂, 02). Which category should we decide on when maximum-likelihood estimation is employed to make the prediction?arrow_forwardConsider the challenge of determining whether a witness questioned by a law enforcement agency is telling the truth. An innovative questioning system pegs two individuals against each other. A reliable witness can determine whether the other individual is telling the truth. However, an unreliable witness's testimony is questionable. Given all the possible outcomes from the given scenarios, we obtain the table below. This pairwise approach could then be applied to a larger pool of witnesses. Answer the following: 1) If at least half of the K witnesses are reliable, the number of pairwise tests needed is Θ(n). Show the recurrence relation that models the problem. Provide a solution using your favorite programming language, that solves the recurrence, using initial values entered by the user.arrow_forward1. Consider an impulse response h[n] such that h[n] = 0 for n < 0 and n > M, and h[n] =−h[M − n] for 0 ≤ n ≤ M where M is an odd integer.a) Express the Fourier transform of h[n] in the formH(ejω) = ejf(ω)A(ω) ,where f(ω) and A(ω) are real-valued functions of ω. Determine f(ω) and A(ω).b) Provide an example of such an impulse response h[n] for M = 7 and find the corresponding f(ω) and A(ω).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole