计量经济学的一些题目.1.Suppose Yi,i = 1,2,…,N,is independently and identically distributed as N(0,σ^2)求:a):Show that E(Yi^2 / σ^2)=1b):Show that W=(1/σ^2) * ∑i=1,N * Yi^2 is distributed λ^2N (ps:λ是很像X的那个希腊字母,N
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![计量经济学的一些题目.1.Suppose Yi,i = 1,2,…,N,is independently and identically distributed as N(0,σ^2)求:a):Show that E(Yi^2 / σ^2)=1b):Show that W=(1/σ^2) * ∑i=1,N * Yi^2 is distributed λ^2N (ps:λ是很像X的那个希腊字母,N](/uploads/image/z/5952311-71-1.jpg?t=%E8%AE%A1%E9%87%8F%E7%BB%8F%E6%B5%8E%E5%AD%A6%E7%9A%84%E4%B8%80%E4%BA%9B%E9%A2%98%E7%9B%AE.1.Suppose+Yi%2Ci+%3D+1%2C2%2C%E2%80%A6%2CN%2Cis+independently+and+identically+distributed+as+N%280%2C%CF%83%5E2%29%E6%B1%82%3Aa%29%3AShow+that+E%28Yi%5E2+%2F+%CF%83%5E2%29%3D1b%29%3AShow+that+W%3D%281%2F%CF%83%5E2%29+%2A+%E2%88%91i%3D1%2CN+%2A+Yi%5E2+is+distributed+%CE%BB%5E2N+%28ps%3A%CE%BB%E6%98%AF%E5%BE%88%E5%83%8FX%E7%9A%84%E9%82%A3%E4%B8%AA%E5%B8%8C%E8%85%8A%E5%AD%97%E6%AF%8D%2CN)
计量经济学的一些题目.1.Suppose Yi,i = 1,2,…,N,is independently and identically distributed as N(0,σ^2)求:a):Show that E(Yi^2 / σ^2)=1b):Show that W=(1/σ^2) * ∑i=1,N * Yi^2 is distributed λ^2N (ps:λ是很像X的那个希腊字母,N
计量经济学的一些题目.
1.Suppose Yi,i = 1,2,…,N,is independently and identically distributed as
N(0,σ^2)
求:
a):Show that E(Yi^2 / σ^2)=1
b):Show that W=(1/σ^2) * ∑i=1,N * Yi^2 is distributed λ^2N (ps:λ是很像X的那个希腊字母,N是下标.)
c):Show that E(W) = N.
怕打的不清楚..附了张题目..
计量经济学的一些题目.1.Suppose Yi,i = 1,2,…,N,is independently and identically distributed as N(0,σ^2)求:a):Show that E(Yi^2 / σ^2)=1b):Show that W=(1/σ^2) * ∑i=1,N * Yi^2 is distributed λ^2N (ps:λ是很像X的那个希腊字母,N
1、E(Yi^2 / σ^2)=E(Yi^2) / σ^2= σ^2 / σ^2=1
2、对于任意一个i,变量Yi/ σ服从标准正态分布N(0,1),则由卡方定义知道,诸Yi/ σ的平方和服从自由度为N的卡方分布
3、卡方分布的定义:服从卡方分布的随机变量的均值为N.