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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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I need help with 1,2 and 3 

**Objective:** Demonstrate the Central Limit Theorem (CLT) through simulation and random sampling. **Background:** If a random variable \(X\) follows a discrete uniform distribution between \(a\) and \(b\), its mean and standard deviation can be calculated as follows: \[ \mu = \frac{a+b}{2} \quad \text{and} \quad \sigma = \sqrt{\frac{(b-a+1)^2-1}{12}} \] In Excel or Google Sheets, use the function `=RANDBETWEEN()` to generate data that follow a discrete uniform distribution. **Project Instructions:** This is an experiment to illustrate the Central Limit Theorem. 1. **Describe the Central Limit Theorem in your own words.** 2. **Use `=RANDBETWEEN(1, 100)` to create 250 samples of size \(n = 30\)** each by generating random integer (whole) numbers between 1 and 100. **Tip:** To keep the data from changing, select the random numbers you need, and press `Ctrl + C` to copy them, then go to select a cell you want to paste the random numbers, then right click to click **Paste Special > Values (V)**. 3. **Use the formulae provided to compute \(\mu\) and \(\sigma\) of the theoretical distribution.**
Transcribed Image Text:**Objective:** Demonstrate the Central Limit Theorem (CLT) through simulation and random sampling. **Background:** If a random variable \(X\) follows a discrete uniform distribution between \(a\) and \(b\), its mean and standard deviation can be calculated as follows: \[ \mu = \frac{a+b}{2} \quad \text{and} \quad \sigma = \sqrt{\frac{(b-a+1)^2-1}{12}} \] In Excel or Google Sheets, use the function `=RANDBETWEEN()` to generate data that follow a discrete uniform distribution. **Project Instructions:** This is an experiment to illustrate the Central Limit Theorem. 1. **Describe the Central Limit Theorem in your own words.** 2. **Use `=RANDBETWEEN(1, 100)` to create 250 samples of size \(n = 30\)** each by generating random integer (whole) numbers between 1 and 100. **Tip:** To keep the data from changing, select the random numbers you need, and press `Ctrl + C` to copy them, then go to select a cell you want to paste the random numbers, then right click to click **Paste Special > Values (V)**. 3. **Use the formulae provided to compute \(\mu\) and \(\sigma\) of the theoretical distribution.**
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