随机变量X服从二项分布B(3,0,4),求y=x的平方的概率分布,
P(y=0)=0.064P(y=1)=0.288
P(y=4)=0.432
P(y=9)=0.216
绛旓細浜岄」鍒嗗竷鏂瑰樊=NP锛1-P锛夋墍浠x涓猴細3*0.5*锛1-0.5锛=3/4 鎵浠锛-2x+1锛=4Dx=3/4*4=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...
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E(x²)=5/3
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X+Y鏈嶄粠B锛92锛0.5锛夌殑浜岄」鍒嗗竷銆傝瘉鏄庢柟娉曟湁涓ょ锛1锛夊彲浠ョ敤鐭╅噺姣嶅嚱鏁帮紝鎶奨鍜孻鐨勭煩閲忔瘝鍑芥暟鍒嗗埆鍐欏嚭鏉ワ紝鐒跺悗鏍规嵁X锛Y鐩镐簰鐙珛杩欎釜鏉′欢锛屾妸涓や釜鐭╅噺姣嶅嚱鏁扮浉涔橈紝鐪嬪嚭鐩镐箻鐨勭粨鏋鏈嶄粠浜岄」鍒嗗竷鐨勫舰寮忓嵆鍙2锛変娇鐢ㄥ畾涔夋潵璇侊紝鍗充簩椤瑰垎甯冩槸鍚勪釜鐙珛鐨勪集鍔埄鍒嗗竷涔嬪拰 X=X1+X2+X3, 鍏朵腑Xi涔嬮棿鏈嶄粠...
绛旓細绛旀鏄3锛璁$畻杩囩▼濡傚浘銆傜粡娴庢暟瀛﹀洟闃熷府浣犺В绛旓紝璇峰強鏃堕噰绾炽傝阿璋紒
绛旓細X鏈嶄粠浜岄」鍒嗗竷B(3,0.1),鍐欏嚭鍒嗗竷鍒楋細0 1 2 3 0.729 0.243 0.027 0.001 杩涜屽氨鍙互鍐欏嚭Y鐨勫垎甯冨垪锛0 1 3 7 0.729 0.243 0.027 0.001 鍥犳锛孍(Y)=0.729*0 + 0.243*1 + 0.027*3 + 0.001*7 =0.243+0.081+0.007 =0.331 鏈変笉鎳傛杩...
绛旓細瀵逛簬绂绘暎鍨闅忔満鍙橀噺锛姹傚叾鍑芥暟鐨鍒嗗竷锛瀹冪殑鍘熺悊鏄滃皢鍙橀噺鐨勬墍鏈夊肩殑鍑芥暟鍊肩畻鍑烘潵锛屾瘡涓嚱鏁板肩殑姒傜巼绛変簬鎵鏈夎兘寰楀埌杩欎釜鍑芥暟鍊肩殑鑷彉閲忕殑姒傜巼鐨勫拰鈥濓紝浣犵湅鐪嬭繖涓師鐞嗚兘涓嶈兘鐪嬫槑鐧姐
绛旓細= Sigma(p(i) * x(i) ^ 2)) - 2* E(X) * Sigma(p(i) * x(i)) + E(X)^2 * Sigma(p(i))= E(X^2) - 2*E(X) * E(X) + E(X) ^ 2 = E(X^2) - E(X) ^ 2 鎵浠ュ鏋滄柟宸笉涓0鐨勮瘽锛孍(X^2) 涓嶦(X)^2鏄笉鍙兘鐩哥瓑鐨勶紙鏂瑰樊绛変簬0鍙嚭鐜板湪鍧囧寑鍒嗗竷涓級
绛旓細浜岄」鍒嗗竷鐨勬暟瀛楃壒寰佸簲璇ユ槸姒傜巼璁轰笌鏁扮悊缁熻涓姹傛帉鎻$殑锛屽畠鐨勬柟宸瓺X锛3脳1/2脳1/2锛3/4