设随机变量X服从二项分布B(3,1/3),则E（x^2）= 设随机变量X服从二项分布B(3,1/3)，则E(X²...
\u8bbe\u968f\u673a\u53d8\u91cfX\u670d\u4ece\u4e8c\u9879\u5206\u5e03B(3,1/3),\u5219E\uff08x^2\uff09=\u60f3\u8981\u95ee\u7684\u662f\u4e0d\u662f\u4e3a\u4ec0\u4e48E(x^2)
\u4e0d\u7b49\u4e8e[E(x)]
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\u662f\u8fd9\u6837\u7684\uff0c\u8bbeP(X
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\u6240\u4ee5\u5982\u679c\u65b9\u5dee\u4e0d\u4e3a0\u7684\u8bdd\uff0cE(X^2)
\u4e0eE(X)^2\u662f\u4e0d\u53ef\u80fd\u76f8\u7b49\u7684\uff08\u65b9\u5dee\u7b49\u4e8e0\u53ea\u51fa\u73b0\u5728\u5747\u5300\u5206\u5e03\u4e2d\uff09
E(x²)=D(x)+E(x)²\uff0cE(x)=np=3\u00d71/3=1\uff0cD(x)=npq=3\u00d71/3\u00d72/3=2/3\uff0cE(x²)=5/3
想要问的是不是为什么E(x^2) 不等于[E(x)] ^ 2是这样的，设P(X = x(i)) = p(i), Sigma表示求和号
方差 = Sigma(p(i) * [x(i) - E(X)] ^2) =
= Sigma(p(i) * x(i) ^ 2)) - 2* E(X) * Sigma(p(i) * x(i)) + E(X)^2 * Sigma(p(i))
= E(X^2) - 2*E(X) * E(X) + E(X) ^ 2
= E(X^2) - E(X) ^ 2
所以如果方差不为0的话，E(X^2) 与E(X)^2是不可能相等的（方差等于0只出现在均匀分布中）
绛旓細D(cx+b)=c^2DX D(-2x+1)=4DX=4*3*(0.5)(1-0.5)=3
绛旓細X鏈嶄粠B(3,0.4)锛屾晠X鍙彇鍊间负0锛1,2,3 褰揦=0鏃讹紝Y=0 褰揦=1,Y=-1 褰揦=2锛孻=0 褰揦=3锛孻=3 鎵浠ワ紝Y鏄釜 绂绘暎鍨闅忔満鍙橀噺 锛屽彲鍙栫殑鍊间负-1,0,3 P锛圷=-1锛=P(X=1)=C(3,1)(0.3)^1*(0.7)^2=0.441 P锛圷=0锛=P锛圶=0)+P锛圶=2锛=0.343+0.189=0.532 P锛...
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绛旓細E(x²)=D(x)+E(x)²锛孍(x)=np=3脳1/3=1锛孌(x)=npq=3脳1/3脳2/3=2/3锛孍(x²)=5/3
绛旓細2锛変娇鐢ㄥ畾涔夋潵璇侊紝鍗浜岄」鍒嗗竷鏄悇涓嫭绔嬬殑浼姫鍒╁垎甯冧箣鍜 X=X1+X2+X3, 鍏朵腑Xi涔嬮棿鏈嶄粠浼姫鍒╋紙p=0.5锛変笖鐩镐簰鐙珛銆俌=Y1+Y2+鈥︹+Y89锛屽叾涓璝i涔嬮棿鏈嶄粠浼姫鍒╋紙p=0.5锛変笖鐩镐簰鐙珛銆傚洜涓篨锛孻鐙珛锛屾墍浠i鍜孻i涔嬮棿涔熺嫭绔嬨俋+Y=X1+X2+X3+Y1+Y2+鈥︹89锛屼簨浠朵箣闂撮兘鏈嶄粠浼姫鍒╋紙p=0.5锛...
绛旓細X鏈嶄粠浜岄」鍒嗗竷B(3,0.1),鍐欏嚭鍒嗗竷鍒楋細0 1 2 3 0.729 0.243 0.027 0.001 杩涜屽氨鍙互鍐欏嚭Y鐨勫垎甯冨垪锛0 1 3 7 0.729 0.243 0.027 0.001 鍥犳锛孍(Y)=0.729*0 + 0.243*1 + 0.027*3 + 0.001*7 =0.243+0.081+0.007 =0.331 鏈変笉鎳傛杩...
绛旓細P锛坹=0)=0.064 P锛坹=1)=0.288 P锛坹=4)=0.432 P锛坹=9)=0.216
绛旓細(1)鐢盤(X鈮1)=5/9锛屽彲寰桺(X=0)=4/9=(1-p)^2,鏁卲=1/3,浠庤 P(Y鈮1)=1-(1-p)^3=26/27 (2)np 涔(1-p)^{n-1}= n(n-1)/2 涔榩^2 涔(1-p)^{n-2}=2涔榥(n-1)(n-2)/6涔榩^3涔(1-p)^{n-3} 瑙ｅ緱n=5, p=1/3 ...
绛旓細鏂瑰樊 = Sigma(p(i) * [x(i) - E(X)] ^2) = = Sigma(p(i) * x(i) ^ 2)) - 2* E(X) * Sigma(p(i) * x(i)) + E(X)^2 * Sigma(p(i))= E(X^2) - 2*E(X) * E(X) + E(X) ^ 2 = E(X^2) - E(X) ^ 2 鎵浠ュ鏋滄柟宸笉涓0鐨勮瘽锛孍(X^2) 涓...
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