(Solved): 5. We want to generate a normal random value from a distribution with mean \( \mu=0 \) and variance ...

5. We want to generate a normal random value from a distribution with mean \( \mu=0 \) and variance \( \sigma^{2}=1 \) using the convolution method. We generate 12 uniform \( (0,1) \) values \( u_{i}, i=1,2, \ldots, 12 \), and find their sum is \( 7.13 \). (a) [1 point] What normal random value is generated? (b) [2 points] Suppose we compute \( w_{i}=1-u_{i} \) from the same 12 uniform values, \( u_{i} \). These would also be uniform \( (0,1) \) random variables. If we had used the \( w_{i} \) to generate the normal value instead of the \( u_{i} \). what would its value be? (c) [1 point] Use the answer from (a) to generate a random normal with mean \( \mu=-2 \) and variance \( \sigma^{2}=4 \).