Let Z1, Z2, ....be iid Normal(0; 1) rvs. Briefly explain how to use these rvs togenerate/construct a rv from the distributions in the list below. You may (and should) use the results fromearlier subproblems in order to solve later subproblems. You are not allowed to use the inverses of cdfs unlessyou can nd them in closed form (without integrals in the nal answer, i.e., of the Normal and Gammadistributions). Justify all your answers.1. Normal( mu = 1; sigma^squared= 4) 2. Chi squared with 1 degree of freedom 3.Chi squared distribution with n degrees of freedom4. Exponential(1)5. Uniform(0,1) 6. Exponential(B = 17) 7. Gamma(k; B= 19), k is a positive integer8. Cauchy distribution

Let Z1, Z2, ….be iid Normal(0; 1) rvs. Briefly explain how to use these rvs togenerate/construct a rv from the distributions in the list below. You may (and should) use the results fromearlier subproblems in order to solve later subproblems. You are not allowed to use the inverses of cdfs unlessyou can nd them in closed form (without integrals in the nal answer, i.e., of the Normal and Gammadistributions). Justify all your answers.1. Normal( mu = 1; sigma^squared= 4) 2. Chi squared with 1 degree of freedom 3.Chi squared distribution with n degrees of freedom4. Exponential(1)5. Uniform(0,1) 6. Exponential(B = 17) 7. Gamma(k; B= 19), k is a positive integer8. Cauchy distribution

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