季同學
2023-04-21 14:25老師可以寫一下這里cov（ax+by，cx+dy）的詳細變形過程嗎
所屬：FRM Part I > Foundations of Risk Management 視頻位置 相關(guān)試題
來源： 視頻位置 相關(guān)試題
1個回答
Lucia助教
2023-04-21 18:02
該回答已被題主采納
同學你好
cov(ax+by,ax+by)
=E[ax+by-E(ax+by)]E[ax+by-E(ax+by)]
=E[(ax-E(ax))+by-E(by)]E[(ax-E(ax))+by-E(by)]
=E[(ax-E(ax)(ax-E(ax)]+E[(ax-E(ax)by-E(by)]+E[by-E(by)(ax-E(ax)]+E[by-E(by)by-E(by)]
=cov(ax,ax)+cov(ax,by)+cov(by,ax)+cov(by,by)
=a2σx2+2abcov(x,y)+b2σy2
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