So that your time can be spent productively working on the problem set as opposed to struggling with MATLAB^® and statistical quandaries, below are a few pieces of information that you might find helpful.

· The MATLAB^® function that generates Gaussian noise is randn. By default, randn creates Gaussian random numbers with zero mean and standard deviation of one.

· To scale the standard deviation of a Gaussian random variable by some factor, k, you simply need to multiply by k. For example, if you want 1000 random numbers from a Gaussian distribution with a standard deviation of 5, in MATLAB^®, you would simply write n = 5*randn(1000,1). This creates a column vector of 1000 random numbers whose standard deviation is 5 and whose mean is zero.

· The MATLAB^® function for a Uniformly distributed RV is rand. By default, rand generates Uniformly distributed random numbers between 0 and 1. Consequently, the mean value of a set of Uniformly distributed RVs generated by rand is 0.5. It is also easily shown that their standard deviation is . Thus, to properly generate uniformly distributed RVs with zero mean and standard deviation k, you must perform two operations. First, you must de-mean the random numbers by subtracting their expected value, 0.5. Second, you must multiply the random numbers by to achieve the desired standard deviation. For example, suppose you want a vector of 1000 Uniformly distributed RVs of mean zero and standard deviation 5. In MATLAB^®, you would write n = 5*(6/sqrt(3))*(rand(1000,1) - 0.5);