Let Z1, Z2, . . . be iid N ormal(0, 1) rvs. Briefly describe how to use these rvs togenerate/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 find them in closed form (without integrals in the final answer, i.e., of the Normal and Gamma distributions).

1. Normal(µ = 1, σ^2 = 4)

2. χ2 with 1 degree of freedom

3. χ2 with n degrees of freedom

4. Exponential(1)

5. Uniform(0,1)

6. Exponential(β = 17)

7. Gamma(k, β = 19), k is a positive integer