Problem 4Throughout this problem, consider the following setting:rng('default') % Set the random number generator to the default seedA first order autoregressive model (AR(1)) can be defined in the following way.3₁=P-1+1=1,2,....T.where y, denotes the value of y at time . p is a parameter and u, is a random variable that has astandard normal distribution. When p=1, the model is called the random walk model. Assumethat yo0 (when t-0), and T-200. Use a for loop to generate 200 observations according this modelwhen p= 1 and p=0.7. Plot your resulting observations in both cases. Your code snippet should generatethe figure given below. Recall that the normrnd function can be used to generate random numbers from thestandard normal distribution% Solution20151020240Random walk versus AR(1)Пилинмымзаличани60 80 100 120 1401pay0.7hany160 180200

For this question, I am using MATLAB Code to Plot the graph.

Throughout this problem, consider the following setting: rng('default') % Set the random number generator to the default s A first order autoregressive model (AR(1)) can be defined in the following way. 3₁=PY₁-1+₁=1,2,....T.

Throughout this problem, consider the following setting: rng('default') % Set the random number generator to the default s A first order autoregressive model (AR(1)) can be defined in the following way. 3₁=PY₁-1+₁=1,2,....T.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.5: Random Variables, Mean, Variance, And Covariance

Problem 5P

See similar textbooks

Similar questions

We are given the following: D = set of all students at your school M(s) = “s is a math major” C(s) = “s is a computer science student” E(s) = “s is an engineering student” Use quantifiers, variables, and the predicates M(s), C(s), and E(s) to express the statement of “Some computer science students are also math majors”
onsider 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, below is a confusion matrix of all the possible outcomes from a given scenarios, This pairwise approach could then be applied to a larger pool of witnesses. Answer the following: Assume a pool of K witnesses, in which the reliable ones are eager to help solve a case, and the unreliable ones are equally eager to hide the truth. Prove that if more than half of the witnesses are unreliable, the approach outlined above cannot help identifying the reliable witnesses.
NOTE: WRITE IN C# Write a distributed probability random number generator using one of the probability sampling methods (like rejection sampling). Explain the codes and the sampling implementation in detail. Example: İnputs : (3, 0.4) (5, 0.5) Output: Generated random number is 3, it has %40 probability Generated random number is 5, it has %50 probability NOTE: WRITE IN C# NOTE: MAKE A GENERIC SOLUTION THAT APPLIES FOR ANY GIVEN NUMBER AND PROBABILITY. NOT JUST BASED ON THIS EXAMPLE !!!
In R-Studio Problem 2. Find a large set of integers (with at least 10000 observations) representing a sample drawn from real life (i.e., do not generate the numbers using some random number generator). First, explain what the integers correspond to in real life. Then, investigate the distribution of the integers, and also the first and last digits of the integers in this sample (For example, if the data has [34 65], plot the distribution of these numbers and also distribution of [3,6] and [4 ,5] separately). Does any of these digits follow a uniform distribution? Is this expected? If one of them does not follow a uniform distribution, what distribution does it follow? Can you explain why? [You can analyze the image age dataset provided by IMDB Wiki, which contains the ages of actors and actresses whose photos are present in the IMDB database. The data contains 459868 age values in years, ranging from 1 to 99 years.]
In Python, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to…
This problem exercises the basic concepts of game playing, using tic-tac-toe (noughtsand crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3 = 1 and −1 to any position with O3 = 1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval (s) = 3X2(s)+X1(s)−(3O2(s)+O1(s))."Mark on your tree the evaluations of all the positions at depth 2."
Question 2. Use composition approach to simulate the following distributionP = 0.3p1 + 0.7p2,where p1 follows a geometric distribution with mean 2 and p2 follows a Bernoulli distributionwith mean 0.1. Write Python code with n = 10^6. Use the random seed 0. Compute thesimulated mean. # use Spyder
1(a). For an M/M/1 queuing system, write your own function in R to compute andoutput the:1. long-run probability po,p1,…,pn of there being 0,..,n people in the system.2. the values L, Lq, W, Wq, and Wse. The function should return elements with the names probs (vector of po,…,pn), L, Lq, W,Wq, and Wse (does not have to be in this order) The function should take as inputs, lambda (arrival rate), mu (service rate), and n (thenumber of people to compute probabilities for 0,…,n) Note: you are to code the computations for the above on your own, so none of the functionsin the queueing package are to be used. 1(b). Using your function from 1(a), find the values (b)-(f) in the Queuing Theory(M_M_1).
SUCCESSIVE-OVER-RELAXATION Method TROUBLESHOOTING: Fix the errors in the code below and run the script with your modified code function [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % Solves Ax = b by Gauss-Seidel method with relaxation. % USAGE: [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % INPUT: % func = handle of function that returns improved x using % x = starting solution vector % maxIter = allowable number of iterations (default is 500) % epsilon = error tolerance (default is 1.0e-9) % OUTPUT: % x = solution vector % numIter = number of iterations carried out % omega = computed relaxation factor if nargin < 4; epsilon = 1.0e-9; end if nargin < 3; maxIter = 500; end k = 10; p = 1; omega = 1; for numIter = 1:maxIter xOld = x; x = feval(func,x,omega); dx = sqrt(dot(x - xOld,x - xOld)); if dx < epsilon; return; end if numIter == k; dx1 = dx; end if numIter == k + p omega = 2/(1 + sqrt(1 - (dx/dx1)ˆ(1/p))); end end error(’Too many iterations’)
Simulated annealing is an extension of hill climbing, which uses randomness to avoid getting stuck in local maxima and plateaux. a) As defined in your textbook, simulated annealing returns the current state when the end of the annealing schedule is reached and if the annealing schedule is slow enough. Given that we know the value (measure of goodness) of each state we visit, is there anything smarter we could do? (b) Simulated annealing requires a very small amount of memory, just enough to store two states: the current state and the proposed next state. Suppose we had enough memory to hold two million states. Propose a modification to simulated annealing that makes productive use of the additional memory. In particular, suggest something that will likely perform better than just running simulated annealing a million times consecutively with random restarts. [Note: There are multiple correct answers here.] (c) Gradient ascent search is prone to local optima just like hill climbing.…
Correct answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. coordinating, we can observe the number of times some white string meets some dark string. We process the number of sets of distinctively shaded strings that cross rather than the number of convergence focuses, so one convergence point might be counted on numerous occasions if various sets of strings meet at a similar point. In case c is a legitimate shading, let f(c) mean the base number of such convergences out of all conceivable matchings. circle above is portrayed by the shading bwbbbwww. In the wake of coordinating with the spools as displayed, there is one convergence between contrastingly shaded strings. It tends to be demonstrated that it is the base conceivable, so f(bwbbbwww)=1. You are given a string s addressing an incomplete shading, with dark, white, and uncolored spools. A shading c is called s-reachable if you can accomplish it by allocating tones to the uncolored…
Please implement Multinomial Logistic Regression on the following data. Please continue from the given code: