A. Generate and plot the following: 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...

SOLUTION:
A)
1. I generated a 100 random observations from N (0, 1). Let
X1 denote these observations. Then the code for plotting
its histogram and computing its mean and variance in
matlab is:
% Run the following in matlab
x1=normrnd(0,1,100,1); % generates 100 observations from
N(0,1)
hist(x1)
m1=mean(x1)% computes mean of x1
v1= var(x1)% computes variance of x1


Here the histogram turns out as shown in the figure above
and the mean and variances are:
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
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Mean= m1= 0.1149
Variance = v1= 0.8680
2) I then generated 100 observations from U[-1,1] and
stored them in a variable named X2. And then obtain the
following results on histogram, mean and variance by
running the following code:
% Run the following in matlab
x2=unifrnd(-1,1,100,1); % generates 100 observations from
U(-1,1)
hist(x2)
m2=mean(x2)% computes mean of x2
v2= var(x2)% computes variance of x2

Mean m2= 0.0560
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
0
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16
Variance v2=0.3529
3) I then generated 100 observations from exponential
distribution with mean 100 and stored them in a variable
named X3. And then obtain the following results on
histogram, mean and variance by running the following
code:
% Run the following in matlab
x3=exprnd(100,100,1); % generates 100 observations from
exponential with mean 100
hist(x3)
m3=mean(x3)% computes mean of x1
v3= var(x3)% computes variance of x1
0 100 200 300 400 500...