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).
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.