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1. Use the rnorm() function to generate a random sample of size N = 50 from the normal distribution (µ, o²), with u = 23 and o = 3. Record this sample as a vector v. %3D (i) Compute the sample mean of uy of v. (ii) Run a bootstrap procedure, with limit B = 5000, to generate re-samples v, i 1,2,3, ,B. (i) Compute the sample mean replicants u. (iii) Plot a histogram for the sample mean replicants , i= 1,2.B. ... (iv) Compute the bootstrap bias bias(uv) and the bootstrap standard error SE(t). (v) Theoretical arguments predict that the standard deviation of µy is given by o/VN. Compare this value with the bootstrap standard error computed at (iv).

1. Use the rnorm() function to generate a random sample of size N = 50 from the normal distribution (µ, o²), with u = 23 and o = 3. Record this sample as a vector v. %3D (i) Compute the sample mean of uy of v. (ii) Run a bootstrap procedure, with limit B = 5000, to generate re-samples v, i 1,2,3, ,B. (i) Compute the sample mean replicants u. (iii) Plot a histogram for the sample mean replicants , i= 1,2.B. ... (iv) Compute the bootstrap bias bias(uv) and the bootstrap standard error SE(t). (v) Theoretical arguments predict that the standard deviation of µy is given by o/VN. Compare this value with the bootstrap standard error computed at (iv).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Use the `rnorm()` function to generate a random sample of size \( N = 50 \) from the normal distribution \(\mathcal{N}(\mu, \sigma^2)\), with \(\mu = 23\) and \(\sigma = 3\). Record this sample as a vector \(\mathbf{v}\). (i) Compute the sample mean of \(\mu_v\) of \(\mathbf{v}\). (ii) Run a bootstrap procedure, with limit \( B = 5000 \), to generate re-samples \(\mathbf{v}^{(i)}, \ i = 1, 2, 3, \ldots, B\). Compute the sample mean replicants \(\mu_v^{(i)}\). (iii) Plot a histogram for the sample mean replicants \(\mu_v^{(i)}, \ i = 1, 2, \ldots, B\). (iv) Compute the bootstrap bias \(\widehat{\text{bias}}(\mu_v)\) and the bootstrap standard error \(\widehat{\text{SE}}(\mu_v)\). (v) Theoretical arguments predict that the standard deviation of \(\mu_v\) is given by \(\sigma/\sqrt{N}\). Compare this value with the bootstrap standard error computed at (iv).
Transcribed Image Text:1. Use the `rnorm()` function to generate a random sample of size \( N = 50 \) from the normal distribution \(\mathcal{N}(\mu, \sigma^2)\), with \(\mu = 23\) and \(\sigma = 3\). Record this sample as a vector \(\mathbf{v}\). (i) Compute the sample mean of \(\mu_v\) of \(\mathbf{v}\). (ii) Run a bootstrap procedure, with limit \( B = 5000 \), to generate re-samples \(\mathbf{v}^{(i)}, \ i = 1, 2, 3, \ldots, B\). Compute the sample mean replicants \(\mu_v^{(i)}\). (iii) Plot a histogram for the sample mean replicants \(\mu_v^{(i)}, \ i = 1, 2, \ldots, B\). (iv) Compute the bootstrap bias \(\widehat{\text{bias}}(\mu_v)\) and the bootstrap standard error \(\widehat{\text{SE}}(\mu_v)\). (v) Theoretical arguments predict that the standard deviation of \(\mu_v\) is given by \(\sigma/\sqrt{N}\). Compare this value with the bootstrap standard error computed at (iv).
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