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Problem 8 [MATLAB exercise] The MA'I'LAB function 'randn' is designed to generate samples of a random variable, say X , which is governed by a unit-Gaussian p.d.f. (i.e., a Gaussian p.d.f. with px = 0 and a} = 1). In this exercise, we will investigate the ability of the routine to generate truly Gaussian samples. (a) Let X be a unit-Gaussian random variable. Using pencil and paper, compute P(0 S X S 0.5) and P(0.9 S X g 1). (b) Use the MATLAB function randn to generate 1000 samples of a unit-Gaussian random variable Let's call the vector X. (c) Use the MATLAB function 'histogram' to create a histogram of the values in X with a bin width of 0.05. ((1) Plot the histogram and comment on the approximation to a unit-Gaussian p.d.f. (9) Use the histogram data to estimate the two probabilities computed in part (a). For example, No. samples in the bin covering the range 0 S X