作者sheep922420 ()
看板Math
标题[机统]求probability distribution
时间Mon Oct 31 14:20:08 2011
X_i be i.i.d N(0,1) random variables i=1,...,k
Y = X_1 + X_2 + ... + X_k
Z = Y^(2)
(1) find the distribution of Y and Z
(2) Evaluate ∫ ( x_1 + x_2 + ... + x_k )^(2) dP_(X_1,X_2,...X_k)(x_1,...x_k)
R^(k)
∫y^(2)P_Y(dy)
R
∫zP_Z(dz)
R+
sol:
P_y ( (-∞,y) )
= P( -∞< Y <=y )
= P(-∞< X_1 + X_2 + ... + X_k <= y)
= P(-∞< X_1 <= x_1) P(-∞< X_2 <= x_2)... P(-∞< X_k <= x_k)
接下来我不知道该怎麽写下去
感谢版上高手
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※ 编辑: sheep922420 来自: 140.117.37.67 (10/31 14:21)
※ 编辑: sheep922420 来自: 140.117.37.67 (10/31 15:04)
1F：→ goshfju :Y建议你用mgf做 10/31 14:54
2F：→ goshfju :你最後一格等号是有问题的 @@ 10/31 14:55
3F：推 TWN2 :Y~N(0,k), Z->chi-square 10/31 14:59