Task $1$: Use Matlab to generate a sufficiently large matrix A of size N $\backslash$times N with IID entries. The entries of

the matrix A can follow the distribution of your choice, except Gaussian.

Hint: Research these functions in Matlab to generate the random matrix entries: exprnd$(),$ rand$(),$ raylrnd$(),...,$ and many more. You

can use any distribution except Gaussian.

Task $2$: Form a vector a $($of size N $\backslash$times $1)$ by selecting the first column of the matrix A$,$ i$.$e$.$ a $=$ A$($:$,1).$ The

entries of this vector should follow the distribution of A$.$

Task $3$: Form a vector z $($of size N $\backslash$times $1)$ by summing the columns $($or rows$)$ of the matrix A$,$ i$.$e$.$ z $=$

sum$($A$).$ The entries of this vector should follow the Gaussian distribution by the CLT$.$

Task $4$:

Use the generated data in Tasks $2$ and $3$ to plot the PDF of a and z$.$

Hint: you may find this Matlab function helpful for this Task histogram$(.).$