1. A histogram for Gaussian "Normal" random variable with zero-mean and unit variance. Calculate its mean and variance.
2. Repeat 1 for a uniformly distributed random variable on the interval [-1,1].
3. Repeat 1 for an exponentially distributed random variable with
B. Apply the following transformations on ::
a. Show the histograms of and
b. Calculate their means and variances and comment on your findings.
C. Verify the central limit theorem by performing the following tasks:
a. Generate 100 Gaussian "Normal" random variables (where each is of zero-mean and unit variance) and add them. Show the histograms for the first and the summed random variables. What is the mean and variance of the resultant random variable?
b. Repeat C(a) but with a sum of 2, 10, 100 random variables that are exponentially distributed with . What is the mean and variance of the resultant random variables, i.e., for the three cases 2, 10 and 100?