Assignment for ECEN 646 Homework 5 Problem 4. Coded in Python.

## Problem:

Let $\{ X_i \}_{i>=1}$ be i.i.d. uniform (0, 1) random variables. Compute the standard deviation $$\sigma$$ of $$X_i$$ and define

$Z_N = \sum_{i=1}^N = \frac{X_i - E[X_i]}{\sigma\sqrt{N}}$

Plot the empirical distribution functions (based on $$10^4$$ random variables) for $$Z_{10}$$, $$Z_{100}$$ and $$Z_{1000}$$. On the same figure plot the distribution function of the standard normal random variable.

## Plot:

$$Z_{10}$$ plot

$$Z_{100}$$ plot

$$Z_{1000}$$ plot

All plot

GitHub repository