Hey Biophysicist,
Here's a question: do existing genes have a lower probability of having a frame shift mutation generate a stop codon than would be expected given a random sequence of nucleotides with nominal proportions of A, C, T, and G bases?
Here's my 2 cent answer
1) Technically coding regions are a random conglomeration of A,C,T, and oh Gs that we happen to care about.
2) I think, and therefore I can be wrong, that random mutations occur equally within coding and non-coding regions, HOWEVER the tolerance for mutations (whether or not they result in a frameshift) is higher and can accumulate in non-coding regions of the DNA.
3) Having said the above it would be difficult for me to prove it since many of these mutations in the coding region would result in spontaneous abortions or actually giving birth to a dead baby (in the animal kingdom).