Imagine that you have a vector of length n. Each of the vectors components is a randomly chosen real number, normal-distributed with mean 0 and standard deviation 1 - N(0,1)-distributed.
What is the expected length of the vector?
I've done a complete derivation for n = 1, and for all even n >= 2. See attachment.
Warning: Not for the faint of heart!
| Attachment | Size |
|---|---|
| paper.a4.pdf | 29.97 KB |