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]

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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