随机变量X～B(2,p),
随机变量X服从二项分布.其分布列为：
X 0 1 2
P (1-p)² p(1-p) p²
P(x=0)=(1-p)²
P(X=1)=C(2,1)P(1-p)
P(X=2)=p².
EX=np=2p.
DX=np(1-p)=2p(1-p).
绛旓細璁闅忔満鍙橀噺X~B(2,p),闅忔満鍙橀噺Y~B(3,1-2p),鑻P(X鈮1)=5/9,鍒欎笅鍒楀叧绯绘垚绔嬬殑鏄憼E(x)>E(Y) 鈶(X)>D(Y)鈶(X)>D(Y) 姹傝В閲 灞曞紑 鎴戞潵绛 浣犵殑鍥炵瓟琚噰绾冲悗灏嗚幏寰: 绯荤粺濂栧姳15(璐㈠瘜鍊+鎴愰暱鍊)+闅鹃濂栧姳20(璐㈠瘜鍊+鎴愰暱鍊)...
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀
绛旓細(1):鍙傛暟P鍊 P{X>=1}=5/9,鎵浠{X
绛旓細鍥犱负X~B(2,p)锛鎵浠3/4=P(X鈮1)=1-P(X=2)=1-p^2锛屾墍浠=1/2锛屽啀鐢盰~B(3,p)鍙緱P(Y鈮2)=1-P(Y=3)=1-p^3=7/8銆
绛旓細D(X)=np(1-p)=2p(1-p)
绛旓細锛P(X鈮1)锛1锛峆(X锛0)锛1锛(1锛p) 2 锛鍗(1锛峱) 2 锛 锛宲锛 .鏁匬(Y锛2)锛滳 3 2 2 1 锛 .
绛旓細鈭闅忔満鍙橀噺鏈嶄粠X锝濨锛2锛孭锛夛紝鈭P锛X鈮1锛=1-P锛圶=0锛=1-C 2 0 锛1-P锛 2 = 7 16 锛屸埓1-P= 3 4 鈭碢= 1 4 鈭碢锛圷=2锛= C 23 ( 1 4 ) 2 脳 3 4 = 9 64 鏁呯瓟妗堜负锛 9 64 ...
绛旓細杩欓噷鐨凜锛2,0锛夋寚鐨勬槸2娆″疄楠岋紝0娆℃垚鍔熴P(x<1)=P(x=0)=(1-p)²c(3,0)鎸3娆″疄楠岋紝0娆℃垚鍔熴備笉鏄庣櫧鍙互杩介棶锛屽鏋滄湁甯姪锛岃閫変负婊℃剰鍥炵瓟锛
绛旓細璁闅忔満鍙橀噺X鏈嶄粠浜岄」鍒嗗竷b锛2锛宲锛夛紝闅忔満鍙橀噺Y鏈嶄粠浜岄」鍒嗗竷b锛4锛宲锛夛紝鑻P锛X鈮1锛夛紳5锛9锛屽垯P锛圷鈮1锛夛紳65锛81銆傚洜涓篜锛圶鈮1锛夛紳5锛9锛屾墍浠ユ弧瓒崇瓑寮廝锛圶鈮1锛夛紳1锛峆锛圶锛0锛夛紳1锛嶏紙1锛峱锛夛季2锛5锛9銆傚寲绠鍙緱P锛1锛3銆傛墍浠ワ紝P锛圷鈮1锛夛紳1锛峆锛圷锛0锛夛紳1锛嶏紙1锛峱锛夛季4...
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