设随机变量x~b(10,0.3),概率最大值点
\u8bbe\u968f\u673a\u53d8\u91cfX~B(3,0.4),\u6c42Y=|X-1|\u7684\u6982\u7387\u5206\u5e03X= 0 1 2 3
Y= 1 0 1 2
\u628aX=0\uff0c2\u5408\u5e76\u5373\u53ef
x~b(3,0.3)
\u6240\u4ee5n=3\uff0cp=0.3
P(X=2)=3C2*0.3^2*(1-0.3)^(3-2)=3*0.09*0.7=0.189
绛旓細鈭璁鹃殢鏈哄彉閲X锝濨锛10锛0.8锛夛紝 鈭碊X=10脳0.8锛1-0.8锛=1.6锛 鈭碊锛2X+1锛=2 2 脳1.6=6.4 鏁呴塁锛
绛旓細浣犲ソ锛佷簩椤瑰垎甯冪殑姒傜巼鏈澶у肩偣鏄痆(n+1)p]锛岃繖閲宯=10锛p=0.3锛(n+1)p=3.3锛屾墍浠ョ瓟妗堟槸3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
绛旓細鏄 E(X)鏈熸湜锛堝钩鍧囧硷級D(X)鏂瑰樊锛堟尝鍔級E(X)=np D(X)=np锛1-p锛塸涓烘鐜囩瓑浜0.3 n涓哄疄楠屾鏁10 鎵浠ラ堿
绛旓細鐢变簬X~B(10,0.3)锛屾牴鎹叕寮忔湁EX=10脳0.3=3,DX=10脳0.3脳0.7=2.1锛屽啀鐢辨湡鏈涗笌鏂瑰樊鐨勬ц川寰桬Y=2EX+1=7锛孌Y=4DX=8.4銆
绛旓細绛旀鏄B锛鍙互鍙嶇敤鏂瑰樊璁＄畻鍏紡鏉ヨ绠楀钩鏂圭殑鏈熸湜銆傝閲囩撼锛岃阿璋紒
绛旓細X~B(30,0.3)E(X)=np = 30(0.3)=9 D(X) =npq =30(0.3)(0.7)=6.3 D(x)=E(X^2)-[E(X)]^2 6.3=E(X^2)-81 E(X^2)=87.3
绛旓細👉浜岄」鍒嗗竷鐨勪緥瀛 銆庝緥瀛愪竴銆 X ~B(10, 0.3)銆庝緥瀛愪簩銆 X ~B(100, 0.4)銆庝緥瀛愪笁銆 X ~B(500, 0.6)👉鍥炵瓟 闅忔満鍙橀噺 X~B(5,0.7)n=5, p=0.7 E(X)=np = 3.5, D(X)= np(1-p)=1.05 鍒╃敤 D(X) = E(X^2) - [E(X)]^2 , 寰楀嚭 E(X^...
绛旓細浣犲ソ锛闅忔満鍙橀噺X~B(10,0.2),Y~e(0.5),鍒欐湁EX=10*0.2=2锛孍Y=1/0.5=2锛屾墍浠(4X-3Y)=4EX-3EY=2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Z=X+Y鐨勬鐜囧瘑搴﹀嚱鏁颁负锛歡(y)=鈭玆 p(x)f(y-x)dx銆=0 y鈮0銆俫(y)=鈭玆 p(x)f(y-x)dx=0 y鈮0銆傗埆[0,y]e^(x-y)dx=1-e^(-y) 0<y鈮1銆俍鐨勬鐜囧瘑搴︼細鈭玔0,1]e^(x-y)dx=e^(1-y)-e^(-y) y>1銆
绛旓細X~b(n,p)鏈嶄粠浜岄」鍒嗗竷锛屽垯E(X)=np E(3x-2)=3Ex-2=3*10*0.2-2=4
