Once again, if I read your implication, , I'm not completely sure if we're on the same page. Your statement is incorrect, but I'm not 100% sure what you are actually saying, so I'll start from the beginning : That N(0,1) you are referring to - that is the distribution that results after standardizing (i'm very sorry - I've been using the word "normalize" in my previous posts) a normal random variable (which yields another normal distribution) and the 1 at the end is the variance of the distribution - not degrees of freedom.

To go down the traditional path of evaluating the probability in question, I would say "yes, as a starting point, you do need to normalize them". This was indeed my first reaction and by the looks of it, that of BGM as well. I'm interested though in hearing what Dragan's viewpoint in this is, seems there is a more direct route.

To use elementary techniques we needs to find distributions for

and

. We can use fact number (2) in BGM's post only if the conditions of number (2) are satisfied, which is that the RV must be normally distributed with mean 0 and variance of 1 (i.e.

) - therefore the standardization. The resulting chi-squared distribution has 1 degree of freedom - this, also, coming from fact (2) in BGM's post.