设X的分布率为X=1 2 3 4,P=0.1 0.2 0.3 0.4,求(1)EX,DX;(2)E(2X-1),D(3X
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设X的分布率为X=1 2 3 4,P=0.1 0.2 0.3 0.4,求(1)EX,DX;(2)E(2X-1),D(3X-10)
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![设X的分布率为X=1 2 3 4,P=0.1 0.2 0.3 0.4,求(1)EX,DX;(2)E(2X-1),D(3X](/uploads/image/z/1648170-18-0.jpg?t=%E8%AE%BEX%E7%9A%84%E5%88%86%E5%B8%83%E7%8E%87%E4%B8%BAX%3D1+2+3+4%2CP%3D0.1+0.2+0.3+0.4%2C%E6%B1%82%281%29EX%2CDX%3B%282%29E%282X-1%29%2CD%283X)
(1)EX=x1p1+x2p2+x3p3+x4p4
=1×0.1+2×0.2+3×0.3+4×0.4
=3
DX=√[(x1-EX)²p1+(x2-EX)²p2+(x3-EX)²p3+(x4-EX)²p4]
=√[(1-3)²×0.1+(2-3)²×0.2+(3-3)²×0.3+(4-3)²×0.4]
=1
(2) E(2X-1)=2EX-1=5
D(3X-10)=3DX=3
=1×0.1+2×0.2+3×0.3+4×0.4
=3
DX=√[(x1-EX)²p1+(x2-EX)²p2+(x3-EX)²p3+(x4-EX)²p4]
=√[(1-3)²×0.1+(2-3)²×0.2+(3-3)²×0.3+(4-3)²×0.4]
=1
(2) E(2X-1)=2EX-1=5
D(3X-10)=3DX=3
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