1. Develop a random variate (composition method) generator for the random variable X with theprobability density function where I represents the indicator function.5f(x)=e*I(x < 0)+e*I(x>0)4a. Implement this generator to generate 500 random variates.b. Compute the sample mean and sample variance of these 500 variates and compare withthe theoretical values.c. Plot the histogram of these 500 variates and compare the histogram with the graph of f(x).

From the given information, fx=46e4xIx<0+56e-xIx>0 Consider, EX=∫-∞0xfxdx+∫0∞xfxdx…

Answered: 1. Develop a random variate…

A First Course in Probability (10th Edition)

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1. Develop a random variate (composition method) generator for the random variable X with the probability density function where I represents the indicator function. 5 e*I(x<0)+=e³I(x>0) 6