QUESTION2PLEASE ANSWER ASAP WITH WORKING THANK YOU Problem 2. John wants to simulate a uniform distribution on the circle of radius R. It turnsout that this is harder to simulate directly using his favorite software package than he thought,so instead he tries simulating a random variable from a uniform distribution over [0, 2π), andthen simulating a distance from the origin D according to the following distribution:0~~ Uniform(0, 2π)2dR²Then these can be used to obtain a point (X, Y). Using the Jacobian method, show that this isa valid way of simulating the uniform distribution over the circle of radius R.fD(d) =

Given that John tries to simulate a random variable from a uniform distribution over and then…

Answered: Problem 2. John wants to simulate a…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 47CR

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2. Find the normal equations to the curve 2* = ax + bx + c %3D 2 = ax+ bx + c
When we take measurements of the same general type, a power law of the form y = αxβ often gives an excellent fit to the data. A lot of research has been conducted as to why power laws work so well in business, economics, biology, ecology, medicine, engineering, social science, and so on. Let us just say that if you do not have a good straight-line fit to data pairs (x, y), and the scatter plot does not rise dramatically (as in exponential growth), then a power law is often a good choice. College algebra can be used to show that power law models become linear when we apply logarithmic transformations to both variables. To see how this is done, please read on. Note: For power law models, we assume all x > 0 and all y > 0.Suppose we have data pairs (x, y) and we want to find constants α and β such that y = αxβ is a good fit to the data. First, make the logarithmic transformations x' = log (x) and y' = log (y). Next, use the (x', y') data pairs and a calculator with linear regression…
Suppose θb is an unbiased point estimator for a parameter θ. We obtain 10,000 different random samples and we compute the value of θb every time. Can we say that θb will underestimate θ a total of 5000 times and it will overestimate θ another 5000 times? What do you expect to see in this experiment?
Answer parts a and b of the following question. Show work. Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. a.) Compute the probability that a patient dies before receiving transplant. b.) Assume that we have θ = 1/10 and µ = 1/15. Use the rexp() function in R for i = 1, 2, . . . , 10000 in simulating death and transplant times for 10,000 patients Xi ∼ Exp(1/10) and Yi ∼ Exp(1/15). What is the proportion of simulated patients who receive transplant before death?
Answer parts a and b of the following question. Show work. Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. a.) In probability/random variable notation, express the probability that a patient receives transplant before death b.) For this problem, what is the joint density fXY (x, y)? Show that it is a valid density.
[Joint PDFS will be covered in Week 7] Let the random variables X and Y be the portions of the time in a day that two alternative routes between Topkapi and Uskudar have congestion (X for Route 1 and Y for Route 2). The joint PDF is given by fx y(x.y) = 2x +y° where 0sx.ys1. (a) Assume g(x) and h(y) are the marginal PDFS of X and Y, respectively. Since fy y(x.y) is not equal to g(x)h(y). it can be concluded that X and Y are not independent. (b) Assume Z=X+Y and W= XY and traffic experts are interested in the expected values of Z and W. E(Z) = |and E(W) = (Simplify your answers. Do not convert fractions into decimals.) (c) Find the variances of X and Y as well as the covariance between them. V(X) = 15 ,V(Y) =| and Cov(X,Y) = (Simplify your answers. Do not convert fractions into decimals.) (d) The variance of Z can be found as V(Z) = (Simplify your answer. Do not convert fractions into decimals.)
The following table contains data from a physics experiment. Complete the table. Trial Rate (m/sec) Time (sec) Distance (m) kq² – 3k1 k1 + 1 k1² + 3k1 + 2 1 k1 3 2 k2 + 6k2 + 5 k2 + 1 2 k22 + 11k2 + 30
EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.
When we take measurements of the same general type, a power law of the form y = ax often gives an excellent fit to the data. A lot of research has been conducted as to why power laws work so well in business, economics, biology, ecology, medicine, engineering, social science, and so on. Let us just say that if you do not have a good straight-line fit to data pairs (x, ý), and the scatter plot does not rise dramatically (as in exponential growth), then a power law is often a good choice. College algebra can-be used to show that power law models become linear when we apply logarithmic transformations to both variables. To see how this is done, please read on. Note: For power law models, we assume all x > 0 and all y > 0. Suppose we have data pairs (x, y) and we want to find constants a and ß such that y = ax is a good fit to the data. First, make the logarithmic transformations x' = log (x) and y' = log (y). Next, use the (x', y') data pairs and a calculator with linear.regression keys…
The following table contains data from a physics experiment. Complete the table. Trial Rate (m/sec) Time (sec) Distance (m) k,² – 3k1 2 k12 + 3k1 + 2 k1 - 3 1 ki + 1 2 k2 + 6k2 + 5 k2 + 1 k2² + 11k2 + 30
Leo used an analog sensor to measure the temperature of his solar panels. After the experiment, he wants to process the data he obtained. Is he allowed to describe the data by using the measures of central tendency? No, because the data he gathered is qualitative in nature. Yes, because the data he gathered is quantitative in nature. No, because the data the gathered is quantitative in nature. Yes, because the data he gathered is qualitative in nature.
Suppose you have the following model. Y = 19 +0.8Yt-1 + Et, where Et ~ WN(0, 4²). The 5-step ahead forecast error variance will be (up to three decimal places)

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