Let X_1,X_2,...,X_n be i.i.d. random variables from N(1,1) distribution. Find the limiting distribution of the ran. var.
W_n = sqrt(n)*[(X_1 + X_2 + ... + X_n - n)] / [((X_1 - 1)^2) + ... + ((X_n - 1)^2)].
We have recently seen this limiting distributions but haven't solved enough problems about it and i don't know which theorem i should apply for a problem(though i guess central limit theorem should work for this problem). Please help me with this. Thanks!