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\end{center}  \end{figure}  \noindent {\bf Problem 2} (only for graduate students) It is known that if   $x$ is a random variable with a pdf $p_x(x)$, i.e., $x \sim p_x(x)$,   and $y$ is a random variable $y \sim p_y(y)$, then   $z=x+y$ is a random variable $z \sim p_z(z)$, where $p_z(z)=p_x(x)*p_y(y)$.   The symbol $*$ denotes the convolution, i.e.,  \begin{equation}  p_z(z)=p_z(x+y)=\int_{-\infty}^\infty p_y(z-x)p_x(x)dx  \end{equation}  (a) If $m_k \sim p(m_k)$, where $p(m_k)$ is depicted in  the figure, and $m_k=n+h$, figure out $p_n(n)$ and   $p_h(h)$.   (b) Use your conclusion from (a) to write a MATLAB code that  generates the sequence from Problem 1. Generate the sequence   100 (or more) times and based on these sequences, verify the  results obtained in Problem 1.  \end{document}