D(X)=E(X^2)-(E(X))^2 3Q
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D(X)=E(X^2)-(E(X))^23QD(X)=E(X^2)-(E(X))^23QD(X)=E(X^2)-(E(X))^23QD(x)=(x1^2-E(x))^2×p1+(x2^2-E(x))^
D(X)=E(X^2)-(E(X))^2 3Q
D(X)=E(X^2)-(E(X))^2 3Q
D(X)=E(X^2)-(E(X))^2 3Q
D(x)=(x1^2-E(x))^2×p1+(x2^2-E(x))^2×p2+……+(xn^2-E(x))^2×pn =x1^2 ×p1-2x1p1E(x)+(E(x))^2×p1+x2^2 ×p2-2x2p2E(x)+(E(x))^2×p2+……+xn^2 ×pn-2xnpnE(x)+(E(x))^2×pn =(x1^2 ×p1+x2^2 ×p2+……+xn^2 ×pn)-(2x1p1E(x)+2x2p2E(x)+……+2xnpnE(x))+((E(x))^2×p1+(E(x))^2×p2+……+(E(x))^2×pn) 考虑到x1p1+x2p2+……+xnpn=E(x) p1+p2+……+pn=1 所以上式D(x)=(x1^2 ×p1+x2^2 ×p2+……+xn^2 ×pn)-2(E(x))^2+(E(x))^2 =E(X^2)-(E(x))^2
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D(x)=E(x^2)-E^2(x)概率公式的推导
D(X)=E(X^2)-(E(X))^2 3Q