# Sampling from Irwin-Hall (Uniform Sum) distribution using rejection sampling

Irwin-Hall Distribution is a probability distribution for a random variable defined as the sum of a number of independent random variables,each having a uniform distribution

True or False: The greater k is (k being the k in $X=\sum_{n=1}^{k}U_n$) The smaller the c you can find so that c must satisfy $f(x) \leq c g(x)$ for all values of x. ($f$ being the density function of the Irwin-Hall distribution and g being the density function of the proposal distribution).

I have a feeling its false because the more uniform random variables we sum, the bigger the variance is and then the bigger the c would need to be to bound f(x) but not sure how to prove it.

• Please add the [self-study] tag & read its wiki. – gung Mar 31 '16 at 14:38
• I suspect you might find the information in the thread on this distribution to be useful. I have no idea what you're actually asking, though, because you haven't told us what $g$ is! – whuber Mar 31 '16 at 15:53
• Thank you for the edit. Since I suspect the answer depends on what $g$ specifically is, do you have a particular proposal distribution in mind? – whuber Apr 1 '16 at 17:23
• I suspect it could be the normal distribution because the density plots look similar , but the normal distribution's support is infinite whereas the support for the Irwin-Hall distribution is finite so I'm not sure what to do with that.. – lfc Apr 1 '16 at 18:18
• Consider any $x$ not in the support: what constraint does that impose on $c$? – whuber Apr 1 '16 at 18:51