若x1,X2···Xn的平均数为X上一横，方差为S的平方，求aX1+b,aX2+b,...,aXn+b的平均数和方差
\u8bbe\u4e00\u7ec4\u6570\u636ex1,x2\u00b7\u00b7\u00b7xn\u7684\u5e73\u5747\u6570x\u62d4\uff0c\u65b9\u5dee\u4e3aS\u5e73\u65b9\u3002\u6c42\uff1aax1,ax2\u00b7\u00b7\u00b7\uff0caxn\u7684\u65b9\u5deex1,x2\u00b7\u00b7\u00b7xn\u7684\u5e73\u5747\u6570x\u62d4 \u90a3\u4e48ax1,ax2\u00b7\u00b7\u00b7\uff0caxn\u7684\u5e73\u5747\u6570\u5c31\u4e3aax\u62d4 \u90a3\u4e48\u65b9\u5dee\u5c31\u4e3a s^2=1/n[\uff08a-ax1\uff09^2+\u2026\u2026(a-axn\uff09^2] \u628aa^2\u63d0\u51fa \u540e\u8fb9\u5c31\u662fs^2 \u90a3\u4e48\u65b9\u5dee\u5c31\u662fas
\u53e6\u4e00\u7ec4\u7684\u5e73\u5747\u6570\u662fx'=(ax1+b+...+axn+b)/n=a(x1+x2+...+xn)/n+nb/n=aX+b
\u65b9\u5deeS'^2=1/n[(ax1+b-aX-b)^2+...(axn+b-aX-b)^2]=1/n[a^2(x1-X)^2+...a^2(xn-X)^2]=a^2S^2
平均数为a(X杠）+b。方差为a平方S.
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