设随机变量x～n(4,2的平方),已知
\u521d\u4e2d\u6570\u5b660\u57fa\u7840\u600e\u4e48\u5b66?\u5bb6\u957f\u7528\u8fd9\u62db\uff0c\u5e2e\u52a9\u5b69\u5b50\u8fc5\u901f\u63d0\u9ad8\u6210\u7ee9 B x=2为中心,即P{X>2}=p{X绛旓細B x=2涓轰腑蹇,鍗砅{X>2}=p{X
绛旓細浼澗鍒嗗竷鐨勫弬鏁板氨鏄湡鏈涘拰鏂瑰樊.D(x)=3 D(y)=np(1-p)=8*1/3*2/3=8/9,E(y)=8/3 D(X-3Y-4)= E(X^2)-E^2(X)+E(9Y^2)-E^2(3Y)=D(x)+D(3Y)=3+8=11
绛旓細N锛2,4锛夋槸鎸噚鏈嶄粠渭 = 2锛屜 = 2鐨姝ｆ佸垎甯冦備篃灏辨槸璇寸洿绾縳=2鏄姝ｆ佸垎甯冨浘鍍忕殑瀵圭О杞达紝鎵浠ワ紝P锝沊鈮2锝=1/6銆傝嫢闅忔満鍙橀噺X鏈嶄粠涓涓暟瀛︽湡鏈涗负渭銆佹柟宸负蟽^2鐨勬鎬佸垎甯冿紝璁颁负N(渭锛屜僞2)銆傚叾姒傜巼瀵嗗害鍑芥暟涓烘鎬佸垎甯冪殑鏈熸湜鍊嘉煎喅瀹氫簡鍏朵綅缃紝鍏舵爣鍑嗗樊蟽鍐冲畾浜嗗垎甯冪殑骞呭害銆傚綋渭 =...
绛旓細N锛2,4锛夋槸鎸x鏈嶄粠渭 = 2锛屜 = 2鐨姝ｆ佸垎甯 涔熷氨鏄鐩寸嚎x=2鏄姝ｆ佸垎甯冨浘鍍忕殑瀵圭О杞 鎵浠ョ洿绾縳=2宸﹀彸鐨勬鐜囦釜鍗犱竴鍗婏紝鍗砅锝X鈮2锝=1/2
绛旓細DY=16銆傝В绛旇繃绋嬪涓嬶細鍥犱负 X ~ N锛2锛4锛夛紱鎵浠 D(X) = 4锛汥(Y)= D(3-2x)= (-2)^2*D(X)= 4*4 =16
绛旓細鎬ц川锛氳嫢X~N(渭,蟽²)锛屽垯(X-渭)/蟽~N(0,1)鎶婂畠鍖栨垚鏍囧噯姝ｆ佸垎甯冿紝渭=2锛蟽=2锛孭{X<3}=P{(X-2)/2<(3-2)/2}=P{(X-2)/2<0.5}=桅(0.5)桅(0.5)鐨勫奸鐩噷搴旇浼氱粰
绛旓細a=2 x灞炰簬姝ｆ佸垎甯冿紝姝ｆ佸垎甯冪殑姒傜巼瀵嗗害鏄互鐩寸嚎x=渭瀵圭О鐨勶紝杩欓噷渭=2 P锛圶>a)=0.5锛屾墍浠鍒氬ソ鏄湪渭杩欎釜鐐癸紝鎵浠=2
绛旓細闅忔満鍙橀噺X~N锛2锛4锛夛紝鎵浠锛圶)=4,D(0.5X)=0.5*0.5D(X)=0.25D(X)=1
绛旓細鍥炵瓟锛X N(2,4) 鍒: EY = aEX + b =2a + b = 0 DY= a²DX = 4a² =1 a = 1/2 b = -1
绛旓細瑙ｏ細E(ax+b)=a*E(x)+b=2a+b=0锛汥(ax+b)=a^2*D(x)=4a^2=1锛涙晠a=1/2锛b=-1 鎴 a=-1/2锛宐=1 鏂瑰樊鍏紡鏄竴涓暟瀛﹀叕寮忥紝鏄暟瀛︾粺璁″涓殑閲嶈鍏紡锛屽簲鐢ㄤ簬鐢熸椿涓悇绉嶄簨鎯咃紝鏂瑰樊瓒婂皬锛屼唬琛ㄨ繖缁勬暟鎹秺绋冲畾锛屾柟宸秺澶э紝浠ｈ〃杩欑粍鏁版嵁瓒婁笉绋冲畾銆
