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  {\LARGE\bf EE342 Spring 1998} \\
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  {\Large\bf Problem Set 4} \\
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  \bf due 2/27\\
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{\bf 1)} Leon-Garcia Chapter 3 \#20, \#44, \#57a,b, \#70, \#80, \#81.


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{\bf 2)} Use matlab to make plots of the pdf and CDF of an exponential
random variable with $\lambda =1$.
Use matlab to compute the mean and variance of the
random variable.  Repeat for an exponential RV with $\lambda = 2$.  

{\bf 3)} Use matlab to make plots of the pdf and CDF of a Gaussian 
random variable with zero mean and unit variance.  
Use matlab to compute the mean and variance of the
random variable.  Repeat for a Gaussian RV with mean one and variance four.  

{\bf 4)}
Use matlab to generate 10000 uniform random numbers.  Let $X$ denote
the uniform random variable.  In the following we generate 10000 RVs
drawn from $Y$ and  $Z$.
\begin{description}
\item[a)] Let $Y=- {\rm ln} (X)$.
\item[b)] Let $Z= \sin (\pi X/2)$.
\end{description}
For $Y$ and $Z$ find the sample mean and variance and plot the
sample pdf and CDF.  Compare with the actual means, variance, pdfs, and CDFs.

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