Question

USING MATLAB

(A) Use the rand command to generate “X” of size [10000 1] and the command histogram to plot the probability distribution of “X” along with axis labels and a title that includes the mean and variance for “X”. (B) Use a while loop and the rand command to generate “X1”, also of size [10000 1] but with each element of “X1” being the mean of 2 “samples” generated using rand, i.e. a “sample size” of 2 separate numbers generated using rand that are then averaged. This is repeated until “X1” is of size [10000 1].

Answer #1

% Matlab script to create random vectors and plot probability
distribution

% A

% generate X of size [10000 1]

X = rand(10000, 1);

% histogram to plot the probability distribution of "X"

histogram(X);

% specify the X and Y labels

xlabel('X');

ylabel('Y');

% specify the title containing the mean and variance of X

txt = sprintf('Mean: %f Variance: %f',mean(X), var(X));

title(txt);

%B

% create X1 of size [10000 1]

X1 = zeros(10000,1);

i=1; % set i to 1

% loop over X1 vector, generating elements for X1

while(i <= length(X1))

samples = rand(2,1); % generate a sample size of 2 using rand

X1(i) = mean(samples); % set ith element of X1 to average of the
samples

i = i + 1;

end

%end of script

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