# Statistic-Beta distribution.

‪Hi. Statistics question.‬

‪I am trying to show that the limiting distribution (the limit of the distribution when $$n\rightarrow\infty$$) of $$\sqrt{n} (B(\lfloor n/2\rfloor, n-\lfloor n/2\rfloor+1)-1/2)$$ is $$N(0,1/4)$$, where B is the Beta distribution and N is the normal distribution.‬

Wikipedia claims there is an expression of the Beta distribution as a quotient of sums of independent exponential distributions but I don't know how to prove this or how to go from there. I am thinking there must be an easy approach through CLT and such, but I don't seem to find it.

Any help on this problem would be greatly appreciated!