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Let Z1, Z2, .be iid Normal(0; 1) rvs. Briefly explain how to use these rvs to generate/construct a rv from the distributions in the list below.

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

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