Simulation of X random variates:
The below distribution of random variates were simulated using MATLAB routines and the envelope rejection methods. The simulated distributions are:
- Normal distribution with mean = 2 and variance =2
- Uniform distribution with a=2, b=4
- Exponential distribution with lambda=2 The mean and the variance for these distributions are computed, plotted and compared for difference between the simulated values and the theoretical values.
Simulation of Y random variates:
The Y random variates are the obtained by transforming the X variates for the respective distribution. Transformation function definition can be found in the report and the code is implemented for different sample sizes of 100,1000 and 10000.
Convergence of Random Variables:
A GUI was created to showcase the different convergences of Y towards its mean value. The convergences that are showcased are:
- Convergence in probability of Y towards it mean
- Almost sure convergence of Y towards its mean
- Mean Square convergence of Y towards its mean
- Convergence in distribution of Y towards X Also, the Weak Law of Numbers for the X variates is demonstrated in the same GUI.