[商管] [統計] 96政大風管(精算組)

[Wei2008 (Wei)]

http://small.lib.nccu.edu.tw/exam/data/master/ins/ins96.pdf
精算組的第二題

2.Let X1, X2,..., be independent identical distributed random variable
  with N(0,1)
  (a) Determine the limiting distribution of the ramdom variable

     Wn = √n(X1 + X2 +  .... + Xn)
            ------------------------
             X1^2 + X2^2 +....+ Xn^2

謝謝。

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 123.192.168.194
推 bboylu:t
推 jaychouyo:N(0,1)
→ jaychouyo:分子寫成(X1+...+Xn)/√n  d收斂到N(0,1)
→ jaychouyo:分母寫成(X1^2 + X2^2 +....+ Xn^2)/n  p收斂到1
→ jaychouyo:相除用Slutsky d收斂到N(0,1)
→ LITTLEN:分子用CLT 分母用 Law of large number 然後slutzky...
→ Wei2008:謝謝~~