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).

Given that a random sample of size N=50 from the normal distribution Nμ, σ2, with μ=23 and σ=3.

Answered: 1. Use the rnorm() function to generate…

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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