Instructions Define S SR 1 Xi where Xi\'s are identically and independently dist
ID: 3224410 • Letter: I
Question
Instructions Define S SR 1 Xi where Xi's are identically and independently distributed (ID) as uniformla, b] Central Limit Theorem: Let Xi's be IID rv's with finite mean pu and finite variance o 2. Then for every real number 2. lim Pr{ where (z) is the normal cDF, i e., Gaussian distribution with mean o and variance 1. e 7 dy. In this homework you will run a program to observe the Central Limit Theorem. 1. Plot the normal CDF using its closed form expression. Note: no need for simulation here, just plotting a function. 2. Repeat the following for "a -1, b-1", "a -5, b 5", "a -10, b 10": For X, Uniform a, bl, run a program to simulate rv and plot its simulated CDF for large enough n until it starts to resemble the normal CDF. Such as the following plot in "Stochastic Processes: Theory for Applications" by Robert G. Gallager:Explanation / Answer
The reason why we need larger n for the CDF to converge as b-a increases is because as this range increases, the variance increases and to cover such a range, we would require more observations.