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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.

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  • $\begingroup$ Please add the [self-study] tag & read its wiki. $\endgroup$ – gung Mar 31 '16 at 14:38
  • $\begingroup$ 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! $\endgroup$ – whuber Mar 31 '16 at 15:53
  • $\begingroup$ 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? $\endgroup$ – whuber Apr 1 '16 at 17:23
  • $\begingroup$ 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.. $\endgroup$ – lfc Apr 1 '16 at 18:18
  • $\begingroup$ Consider any $x$ not in the support: what constraint does that impose on $c$? $\endgroup$ – whuber Apr 1 '16 at 18:51

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