设随机变量X、Y相互独立,且X~N(1,9)，Y~U（2,4），则E（X+Y）= 设随机变量X与Y相互独立,且X~U(0,2),Y服从参数为3...
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p(x)= 1 x\u2208(0,1)
0 \u5176\u4ed6
Y\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3a
f(x)= e^(-x) x\u22650
0 \u5176\u4ed6
\u5229\u7528\u548c\u7684\u5206\u5e03\u516c\u5f0f\u53ef\u77e5,Z\u7684\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u4e3a
g(y)=\u222bR p(x)f(y-x)dx
=0 y\u22640
\u222b[0,y]e^(x-y)dx=1-e^(-y) 01
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X~U(0,2)\uff0c E(x)=(0+2)/2=1
Y\u670d\u4ece\u53c2\u6570\u4e3a3\u7684\u6307\u6570\u5206\u5e03\uff0cE(Y)=1/3
\u968f\u673a\u53d8\u91cfX\u4e0eY\u76f8\u4e92\u72ec\u7acb\uff0cE(XY)=E(X)*E(Y)=1*(1/3)=1/3
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E(X)=1, D(X)=9
Y~U(2,4)
E(Y) = (1/2)(4+2) = 3
E(Y^2) = (1/2) ∫(2->4) y^2 dy = (1/6)[ y^3 ] |(2->4) = 56/6 = 28/3
D(Y) = E(Y^2) -[E(Y)]^2 = 28/3 -9 = 1/3
E（X+Y）=E(X)+E(Y) = 1+3 =4
D(X+Y) = D(X) + D(Y) = 9 + 1/3 = 28/3
绛旓細X-Y~N(-1锛5)銆傜敱宸茬煡寰桬X=0锛孌X=1锛孍Y=1锛孌Y=4锛屼簬鏄疎(X-Y)=EX-EY=-1锛X锛孻鐩镐簰鐙珛锛屾墍浠(X-Y)=DX+D(-Y)=DX+DY=5銆傛晠X-Y~N(-1锛5)
绛旓細銆愮瓟妗堛戯細E(X)=1,D(X)=1;E(Y)=-2,D(Y)=1.鍥犳E(2X+Y)=2E(X)+E(Y)=2脳1+(-2)=0,D(2X+Y)=22D(X)+D(Y)=4脳1+1=5.
绛旓細銆愮瓟妗堛戯細
绛旓細e(z)=e(2x-y)=2e(x)-e(y)=2-0=2 d(z)=d(2x-y)=4d(x)+d(y)=4(2)+1=9 鎵浠=2X-Y+3=(2,9)涓涓簩缁存鎬2113鍒嗗竷鐨勮竟缂樺垎甯冪殑鍜屾绘槸姝ｆ佸垎甯冦傜壒鍒殑涓や釜鐙珛姝ｆ佸垎甯冪殑鍜屾绘槸姝ｆ佸垎甯冦
绛旓細銆愮瓟妗堛戯細D 鐢变簬鍙橀噺X鍜孻鐩镐簰鐙珛锛屽垯 E锛圸锛夛紳E锛圶锛媃锛夛紳E锛圶锛夛紜E锛圷锛夛紳渭1锛嬑2D锛圸锛夛紳D锛圶锛媃锛夛紳D锛圶锛夛紜D锛圷锛夛紳蟽12锛嬒22鏁匷锝濶锛埼1锛嬑2锛屜12锛嬒22锛夈
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绛旓細闅忔満鍙橀噺X涓Y鐩镐簰鐙珛锛E(XY)=E(X)*E(Y)=1*(1/3)=1/3 鎸囨暟鍒嗗竷涓庡垎甯冩寚鏁版棌鐨勫垎绫讳笉鍚岋紝鍚庤呮槸鍖呭惈鎸囨暟鍒嗗竷浣滀负鍏舵垚鍛樹箣涓鐨勫ぇ绫绘鐜囧垎甯冿紝涔熷寘鎷鎬佸垎甯冿紝浜岄」鍒嗗竷锛屼冀椹垎甯冿紝娉婃澗鍒嗗竷绛夌瓑銆傚鏋滀竴涓殢鏈哄彉閲忓憟鎸囨暟鍒嗗竷锛屽綋s,t>0鏃舵湁P(T>t+s|T>t)=P(T>s)銆傚嵆锛屽鏋淭鏄煇涓...
绛旓細E(X+Y) = E(X)+E(Y) = -1+1 =0 D(X+Y) = D(X)+D(Y) = 1+3 = 4 X+Y ~ N (0, 4)P(X+Y>2)=P(Z > (2-0)/2 )=P(Z >1)
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