设随机变量X~B(2,p),Y~B(3,p),若P(X≥1)=34,则P(Y≥1) 设随机变量X~B(2,p),随机变量Y~B(3,p),若P(...
3.\u8bbe\u968f\u673a\u53d8\u91cfx ~ b(2,p),y~ b(3,p),\u82e5p{x\u2265l}=\u4e8c,\u6c42p{y\u22651}.P{X\u22651}=1-P{X=0}=1-(1-p)²=5/9
\u2234p=1/3
\u2234P{Y\u22651}=1-P{Y=0}=1-(1-p)³=1-(1-1/3)³=19/27
\u6216
P(X\u22651)=1-P(X=0)=1-C(2 0)*(p^0)(1-p)^2=1-(1-p)^2=3/4
p=1/2
p(y\u22651)=1-P(Y=0)=1-C(3 0)*(p^0)(1-p)^3=7/8
\u8fde\u7eed\u578b
\u8fde\u7eed\u578b\uff08continuous\uff09\u968f\u673a\u53d8\u91cf\u5373\u5728\u4e00\u5b9a\u533a\u95f4\u5185\u53d8\u91cf\u53d6\u503c\u6709\u65e0\u9650\u4e2a\uff0c\u6216\u6570\u503c\u65e0\u6cd5\u4e00\u4e00\u5217\u4e3e\u51fa\u6765\u3002\u4f8b\u5982\u67d0\u5730\u533a\u7537\u6027\u5065\u5eb7\u6210\u4eba\u7684\u8eab\u957f\u503c\u3001\u4f53\u91cd\u503c\uff0c\u4e00\u6279\u4f20\u67d3\u6027\u809d\u708e\u60a3\u8005\u7684\u8840\u6e05\u8f6c\u6c28\u9176\u6d4b\u5b9a\u503c\u7b49\u3002\u6709\u51e0\u4e2a\u91cd\u8981\u7684\u8fde\u7eed\u968f\u673a\u53d8\u91cf\u5e38\u5e38\u51fa\u73b0\u5728\u6982\u7387\u8bba\u4e2d\uff0c\u5982\uff1a\u5747\u5300\u968f\u673a\u53d8\u91cf\u3001\u6307\u6570\u968f\u673a\u53d8\u91cf\u3001\u4f3d\u9a6c\u968f\u673a\u53d8\u91cf\u548c\u6b63\u6001\u968f\u673a\u53d8\u91cf\u3002
\u8fd9\u91cc\u7684C\uff082,0\uff09\u6307\u7684\u662f2\u6b21\u5b9e\u9a8c\uff0c0\u6b21\u6210\u529f\u3002
P(x<1)=P(x=0)=(1-p)²
c(3,0)\u63073\u6b21\u5b9e\u9a8c\uff0c0\u6b21\u6210\u529f\u3002
\u4e0d\u660e\u767d\u53ef\u4ee5\u8ffd\u95ee\uff0c\u5982\u679c\u6709\u5e2e\u52a9\uff0c\u8bf7\u9009\u4e3a\u6ee1\u610f\u56de\u7b54\uff01
简单计算一下即可,答案如图所示
∵随机变量服从X~B(2,P),∴P(X≥1)=1-P(X=0)=1-
C | 0 绛旓細闅忔満鍙橀噺X锝濨(2,p)锛孭(X>=1)=5/9锛孭(X锛1)=4/9锛滳锛2锛0锛夛紙1锛峱)^2,p锛1/3 P(Y>=1)=1-P(Y<1)=1-C锛3锛0锛夛紙1锛峱)^3=19/27 绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀 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 绛旓細鐢卞凡鐭 鏈P(X<1)=P(X=0)=1-5/9=4/9 = (1-p)²鎵浠=1/3 鑰P(Y>=1)=1-P(Y<1)=1-P(Y=0)=1-(1-p)鍥涙鏂=1-(2/3)鍥涙鏂 = 65/81 绛旓細2016-05-01 闅忔満鍙橀噺X~b(2,p),Y~b(3,p),骞朵笖宸茬煡P(X<... 1 2015-02-04 璁鹃殢鏈哄彉閲廥锝濨(2,p),Y锝濨(3,p),鑻(X鈮1)... 1 2018-08-19 璁鹃殢鏈哄彉閲廥锝濨(2,p),Y锝濨(3,p),鑻(X=0)... 2014-06-15 闅忔満鍙橀噺X~B(2,p),Y~B(4,p),鑻(X>=1)... 2018-01-09 璁鹃殢... 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 绛旓細璁鹃殢鏈哄彉閲廥鏈嶄粠浜岄」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锛宲锛夛紝鑻锛圶鈮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... 绛旓細璁鹃殢鏈哄彉閲廥鏈嶄粠浜岄」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锛宲锛夛紝鑻锛圶鈮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... 绛旓細(1)鐢P(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X-B(2,P),Y-B(3,P),P(X>=1)=1-P(X<1)=1-P(X=0)杩欐牱搴旇鍙互鍋氫簡锛屼粠涓婅堪寮忓瓙涓緱鍒癙锛屽啀姹侾(Y>=1)灏变笉闅句簡銆傘傘 本站交流只代表网友个人观点,与本站立场无关 |