设随机变量X~b(3，0.4)，求Y=X²-2X的分布率

\u8bbe\u968f\u673a\u53d8\u91cfX\u670d\u4ece\u4e8c\u9879\u5206\u5e03B\uff083,0.4\uff09\uff0c\u6c42\u968f\u673a\u53d8\u91cfY=X(X-2\uff09\u7684\u6982\u7387\u5206\u5e03

X\u670d\u4eceB(3,0.4)\uff0c\u6545X\u53ef\u53d6\u503c\u4e3a0\uff0c1,2,3
\u5f53X=0\u65f6\uff0cY=0
\u5f53X=1,Y=-1
\u5f53X=2\uff0cY=0
\u5f53X=3\uff0cY=3
\u6240\u4ee5\uff0cY\u662f\u4e2a\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cf\uff0c\u53ef\u53d6\u7684\u503c\u4e3a-1,0,3
P\uff08Y=-1\uff09=P(X=1)=C(3,1)(0.3)^1*(0.7)^2=0.441
P\uff08Y=0\uff09=P\uff08X=0)+P\uff08X=2\uff09=0.343+0.189=0.532
P\uff08Y=3)=P(X=3)=0.027

\u8fd9\u6837\u5c31\u53ef\u4ee5\u5f97\u5230Y\u7684\u5206\u5e03\u5217\u4e86

E(X²)=D(X)+E²(X)=3+3*3=30
E(Y²)=D(Y)+E²(Y)=1.6+4=5.6
E(2X^2-Y^2)=2E(X²)-E(Y²)==54.4
\u5982\u6709\u610f\u89c1\uff0c\u6b22\u8fce\u8ba8\u8bba\uff0c\u5171\u540c\u5b66\u4e60\uff1b\u5982\u6709\u5e2e\u52a9\uff0c\u8bf7\u9009\u4e3a\u6ee1\u610f\u56de\u7b54\uff01

X的取值为0,1,2,3, 带入可得Y的取值分别为 -1,0,3
P{Y=-1}=P{X=1}=C_3^1(0.4)^1(0.6)^2
P{Y=3}=P{X=3}=C_3^3(0.4)^3(0.6)^0
P{Y=0}=1-P{Y=-1}-P{Y=3}

璁鹃殢鏈哄彉閲廥~B(3, 0.4),, 鍒橮(Y=1)鐨勫间负
绛旓細X~B(3,0.4)锛屽垯P(X=1)=C(3,1)(0.4)(0.6^2)=0.432 P(X鈮1)=1-P(X=0)=1-C(2 0)*(p^0)(1-p)^2=1-(1-p)^2=3/4 p=1/2 p(y鈮1)=1-P(Y=0)=1-C(3 0)*(p^0)(1-p)^3=7/8

璁鹃殢鏈哄彉閲廥~B(3,0.4),涓旈殢鏈哄彉閲廦=(3-X)/2,鍒橢(Y)=
绛旓細E(X)=3脳0.4=1.2 E(Y)=3/2-1/2路E(X)=1.5-0.6=0.9 銆愰檮娉ㄣ戯紙1锛塜~B(n锛宲)锛屽垯 E(X)=np 锛2锛塃(kX+b)=kE(X)+b

璁鹃殢鏈哄彉閲廥锝B(3,0.4)
绛旓細浜岄」鍒嗗竷锛孍x=3*0.4=1.2锛

璁鹃殢鏈哄彉閲廥~B(3,0.4),涓旈殢鏈哄彉閲廦=(3-X)/2,鍒橢(Y)=
绛旓細E(X)=3脳0.4=1.2 E(Y)=3/2-1/2路E(X)=1.5-0.6=0.9 銆愰檮娉ㄣ戯紙1锛塜~B(n,p),鍒 E(X)=np 锛2锛塃(kX+b)=kE(X)+b

闅忔満鍙橀噺X~b(3,0.4)琛ㄧず浠涔 ? 杩欎釜寮忓瓙琛ㄧず浠涔堟剰鎬濆晩 ~~姹傛暀~~
绛旓細X鏈嶄粠鍙傛暟涓3,0.4鐨凚ernoulli鍒嗗竷 鍗冲湪3娆＄嫭绔嬮噸澶嶈瘯楠屼腑,姣忔璇曢獙鎴愬姛鐨勬鐜囦负0.4,鎬荤殑鎴愬姛娆℃暟涓篨鐨勫垎甯 P(X=k)=C(3,k)*0.4^k*0.6^(3-k)

璁鹃殢鏈哄彉閲弜~b(3,0.4)鍒檖(x鈮1)
绛旓細浣犲ソ锛乆鏄簩椤瑰垎甯冿紝鎵浠(X鈮1)=1-P(X<1)=1-P(X=0)=1-0.6^3=0.784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

璁鹃殢鏈哄彉閲廥~B(3,0.4),姹侾{X鈮1}
绛旓細X灞炰簬n锛3,p锛0.4鐨勪簩椤瑰垎甯冿紝鎵浠{X锛0}锛0.6^3锛0.216 P{X鈮1}锛1-P{X锛0}锛0.784 鍥炵瓟瀹屾瘯姹傞噰绾

璁X~B(3,0.4),姹備笅鍒闅忔満鍙橀噺鐨勬暟瀛︽湡鏈
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 褰搙=0鏃讹紝y=0 褰搙=1,y=-1 褰搙=2锛寉=0 褰搙=3锛寉=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锛坹=-1锛=p(x=1)=c(3,1)(0.3)^1*(0.7)^2=0.441 p锛坹=0锛=p锛坸=0)+p锛坸=2锛=0.343+0.189=0.532 p锛坹=...

璁鹃殢鏈哄彉閲廥锝b(3,0.4),涓旈殢鏈哄彉閲廦=X(3-X)/2,鍒檖{X=Y}=
绛旓細鎵惧嚭鑳芥弧瓒虫潯浠剁殑X鍙栧煎嵆鍙眰鍑烘鐜囷紝杩囩▼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

璁鹃殢鏈哄彉閲廥~B(3,0.4),鍒橮(X=0)=
绛旓細鍥炵瓟锛0.6浜岄」鍒嗗竷涓嶆槸杩欎釜灏辨槸閭ｄ釜,鍙湁涓ょ缁撴灉