作者berrylover (看不见看不见我不要看见ꌩ
看板Statistics
标题[问题] 几题多变量的问题
时间Sun Oct 4 22:37:06 2009
suppose X = (x_1, x_2,...x_n), Y = (y_1,...y_n) are independant random vectors
w/ expectation zero and covariance matrix P =(p_ij) and Q = (q_ij),
respectively
(a) find a random vector w/ covariance matrix P+Q
(b) find a random vector whose covariance matrix is the "Hadamard product"
P*Q = (p_ij*q_ij)
(c) suppse n = 2 and p_11,q_22>0. Define the correlation
v_12=p_12/[(p_12*q_12)^1/2]. what does |v_12|=1 imply about the
rank of the covariance matrix and the relationship between X_1 and X_2
(d) Suppose that P is singular. Show that with probablity one X belongs
to lower-dimensional subspace
linear algebra 已经有点不复记忆了 麻烦高人指点
(a) 小题 我的想法是
利用Cov(X)的定义 = E[(X-E(X))(X-E(X))^t], given E(X)=0
thus E(X*X^t)=P, and E(Y*Y^t)=Q likewise
E[(X+Y)-E(X+Y)][(X+Y)-E(X+Y)^t]
=E[(X+Y)*(X^t+Y^t)]
=E(XX^t+XY^t+YX^t+YY^t), given X and Y are independant,
the above will be equal to P+Q....
@@ 矩阵的很多性质要重新念过 写的非常心虚 另外三小题还不知如何下手
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1F：→ bmka:你的想法呢? 10/04 23:09
※ 编辑: berrylover 来自: 99.23.153.209 (10/04 23:26)