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14 MATLAB USAGE AND COMPUTATIONAL ERRORS (A5) It is just a set of function values [f1(x1) f1(x2) . ] obtained at a time for several values [x1 x2. ] of x. ) just before the arithmetic operators *(multiplication), /(division), and ^ (power) in the function deﬁnition so that the term-by-term (termwise) operation can be done any time. Note that we can deﬁne a simple function not only in an independent M-ﬁle, but also inside a program by using the inline() command or just in a form of literal expression that can be evaluated by the command eval().

24 MATLAB USAGE AND COMPUTATIONAL ERRORS >>u_noise1 = 2*u_noise-1 %a 1000x1 noise vector with U(-1,1) >>subplot(222), hist(u_noise1,20) %histogram 2. Random Number with Normal (Gaussian) Distribution The numbers in a matrix generated by the MATLAB function randn(M,N) have normal (Gaussian) distribution with average m = 0 and variance σ 2 = 1, as described by N (0,1). 6) The probability density function of the new Gaussian number generated by this transformation is obtained by substituting x = (y − m)/σ into Eq.

Rand(M,N): generates an M x N matrix consisting of uniformly distributed random numbers randn(M,N): generates an M x N matrix consisting of normally distributed random numbers BASIC OPERATIONS OF MATLAB 23 1. Random Number Having Uniform Distribution The numbers in a matrix generated by the MATLAB function rand(M,N) have uniform probability distribution over the interval [0,1], as described by U(0,1). 1) whose value is 1 over [0,1] and 0 elsewhere. 4) For practice, we make a vector consisting of 1000 standard uniform numbers, transform it to make a vector of numbers with uniform distribution U(−1, +1), and then draw the histograms showing the shape of the distribution for the two uniform number vectors (Fig.