Implement a function in Matlab that simulates observations ofan exponential rand

Question

Implement a function in Matlab that simulates observations ofan exponential random variable. Your function should take as input parameters n andlambda . The output of your function should be a vector of size n x 1 containing n samples drawnfrom an exponential distribution with parameter lambda . Please comment your code liberally. You can use the built in function rand(n,1) in order togenerate n uniformly distributed random numbers. Section 5.4 in the text will explain a general methodfor transforming these into exponentially distributed random numbers.
The methods mentioned in our book are 'The InverseTransformation Method', 'The Rejection Method,' and the 'Box-MullerMethod.' I'm not sure which one is supposed to be used here, norhow to transform the random numbers into an exponentialdistribution with them. Any help would be great. Implement a function in Matlab that simulates observations ofan exponential random variable. Your function should take as input parameters n andlambda . The output of your function should be a vector of size n x 1 containing n samples drawnfrom an exponential distribution with parameter lambda . Please comment your code liberally. You can use the built in function rand(n,1) in order togenerate n uniformly distributed random numbers. Section 5.4 in the text will explain a general methodfor transforming these into exponentially distributed random numbers.
The methods mentioned in our book are 'The InverseTransformation Method', 'The Rejection Method,' and the 'Box-MullerMethod.' I'm not sure which one is supposed to be used here, norhow to transform the random numbers into an exponentialdistribution with them. Any help would be great.

Explanation / Answer

The inverse transformation method is used to convert a uniformrandom distribution over [0, 1] to a distribution of anytype. Given the uniform random variable X and arbitrarydistribution Y with a cdf of F(y), F^(-1)(X) [F inverse of X] hasdistribution of F. In other words, if all we have availableis a set of random numbers between 0 and 1, we can convert thisinto a random distribution of any type by applying the inverse cdfof the distribution to these random numbers. In your case, the cdf is X = 1 - e^(-y). Taking the inverse we get... X = 1 - e^(-Y) 1 - X = e^(-Y) ln(1 - X) = -Y -1/ * ln(1 - X) = Y However, since X is uniform between [0, 1], 1 - X = X Thus, our transform is Y = -1/ * ln(X) function Y = exponential_dist(n, lambda) X = rand(n, 1); %generate nx1 random vector Y = -1/lambda .* ln(X); %transform from uniform to exponential

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