设随机变量X~B(100,0.2),应用中心极限定理可得P{X≥30}≈多少(Φ(2.5)=0.9938) 大学理工科专业都要学高等数学吗?有哪些专业不学?
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1.
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2.
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3.
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4.
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解 E(X)=100*0.2=20,D(X)=100*0.2*0.8=16
于是由中心极限定理得
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
绛旓細浣跨敤涓績鏋侀檺瀹氱悊锛寈鐢1000涓簩椤瑰垎甯冨彲浠ヨ繎浼艰涓烘槸姝f佸垎甯冧簡锛屼綘绠楀嚭浠栫殑鏈熸湜鏂瑰樊 鐒跺悗鎶妜鍖栦负鏍囧噯姝eお鍒嗗竷灏卞ソ楗夸簡
绛旓細1銆丒(X)=np=10路0.2=2 2銆丏(X)=(b-a)^2/12 =36/12 =3
绛旓細1.9銆x鏈嶄粠浜岄」鍒嗗竷B(10锛0.1)锛屾牴鎹叕寮廍X=nP=10*0.1=1DX=nP(1-P)=10*0.1*0.9=0.9=E(X-EX)^2=E(X^2-2x+1)=0.9E(X^2)=0.9+2EX-1=0.9+2-1=1.9E(5X^2+3)=5E(X^2)+3=5*1.9+3=12.5銆侲(X^2-2x+1)=E(X^2)-2EX+1=0.9 绉诲悜鏁寸悊锛孍(X^2)...
绛旓細E(X) =np = 10(0.4)=4 D(X)=np(1-p) = 10(0.4)(0.6) = 2.4 D(X) =E(X^2) -[E(X)]^2 2.4 =E(X^2) -16 E(X^2)=18.4
绛旓細(1)璁句簨浠禔銆丅鐩镐簰鐙珛锛孭锛圓UB锛=0.6锛孭锛圓锛=0.4锛屽垯 P(AUB)=P(A)+P(B)-P(A)P(B)0.6=0.4+P(B)-0.4P(B)0.6P(B) = 0.2 P(B) = 1/3 (2)璁鹃殢鏈哄彉閲廥~B锛400锛0.1锛夛紝D(X)=np(1-p) = 400(0.1)(1-0.1) = 36 (3)X~U锛1锛4锛塜鐨勫瘑搴﹀嚱鏁 f(...
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
绛旓細P(Y=0)=P(X=3)+P(X=0)=0.2^3+0.8^3=0.52婊℃剰璇峰ソ璇勫摝锛屾垜姒傜巼璁鸿冨畬浜嗭紝鍢诲樆锛岀浣犺冭瘯椤哄埄鍟
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