Python

Code 1 Write a script that allows you to obtain 104 random variables (r.v.) exponentially distributed with parameter (e.g., = 0.5), using a generator of uniformly distributed r.v. (e.g., numpy.random.uniform). You are not allowed to use a function that directly generates exponentially distributed r.v. (e.g., numpy.random.exponential). You answer must include: -Your code. - Graphical evidence showing that your output r.v. are exponentially distributed. What quantitative evidence can you provide to support that your results are correct? Code 2 Write a script to verify numerically the central limit theorem (CLT) when you add exponentially distributed r.v. You answer must include: -Your code. - Graphical evidence showing that your output r.v. follow a Gaussian Distribution. What quantitative evidence can you provide to support that your results are correct? Code 3 Write a script to verify numerically that the interarrival times for a Poisson process are exponentially distributed. You answer must include: - Your code. -Graphical evidence showing that your output r.v. follow an exponential distribution. -What quantitative evidence can you provide to support that your results are correct? Code 4 Write a script to verify numerically that a proportionate growth model yields a distribution of object sizes, which is log-normally distributed You answer must include: -Your code. - Graphical evidence showing that your output r.v. follow a log-normal distribution. - What quantitative evidence can you provide to support that your results are correct? Code 5 Write a script to verify numerically that the first return time distribution for a discrete random walk is a power-law. You answer must include: - Your code. - Graphical evidence showing that your output r.v. follow a power-law distribution. - What quantitative evidence can you provide to support that your results are correct?