Trying to find the probability of a sum of standard normal variables being greater than a set value in R

Question

I'm brand new to R, and I'm sure this should be an easy question for some people, but I can't figure it out.

How do I find the probability that an equation of independent standard normal variables is greater than a certain value using R?

Pr((x_1^2 + x_2^2 + x_3^2) > 5)

Answer 1

The random variable x_1^2 + x_2^2 + x_3^2 follows the Chi-squared distribution with 3 degrees of freedom. So your probability is given in R by

pchisq(5, df = 3, lower.tail = FALSE)