Hi, I have a bit trouble proving a part of question 4) and question 5).
For question 4), I can prove that those random variables are independent by showing that the doc product between any two of them is zero. However, for the second part, which is to prove that those random variables follow the normal distribution, I am not sure how to approach it. I know the random error e_i epsilon follows the normal distribution and q_i is a unit vector, but how to prove that their product also follows normal distribution? Any hints will be helpful. Thanks in advance.
For question 5), I guess I just don't know how to prove a random variable follows a certain distribution in general. So I might gain some insights from the help for question 4) and reattempt to solve question 5). Thanks a lot.