设连续型随机变量x在区间【3,5】上服从均匀分布,其密度函数为 ;
密度函数为分段函数:φ(x)=1/2,x∈[3,5];φ(x)=0,x∉[3,5]。只要有密度函数,其余都很容易了吧,自己试试。绛旓細Y鈮1鎵浠²鈮鎵浠(Y²)鈮(Y)鎵浠(X)鈮E(Y)-E²(Y)]脳(b-a)²E(Y)-E²(Y)灏辨槸a-a²杩欑,a-a²=a(1-a)鐢ㄥ潎鍊间笉绛夊紡a(1-a)鈮(a+1-a)²/4=1/4鎵浠(X)鈮1/4脳(b-a)²=(b-a)²/4灏辫瘉瀹屼簡銆傝繖閬撻鏉′欢鍔犲己,璇翠簡X鏄涓杩炵画鍨嬮殢鏈哄彉閲,鍙兘濂借瘉涓鐐...
绛旓細鏍规嵁棰樼洰缁欏嚭鐨勪俊鎭紝杩炵画鍨嬮殢鏈哄彉閲廥鍦ㄥ尯闂(2, 8)涓婃湇浠庡潎鍖鍒嗗竷銆傝姹傛柟绋媡^2 + Xt + 1 = 0鏈夊疄鏍癸紝闇瑕佸垽鏂垽鍒紡螖 = X^2 - 4ac澶т簬绛変簬闆躲傚浜庣粰瀹氱殑鏂圭▼t^2 + Xt + 1 = 0锛屽皢鍏惰浆鍖栦负涓鑸舰寮忥紝寰楀埌at^2 + bt + c = 0锛屽叾涓璦 = 1锛宐 = X锛宑 = 1銆傚垽鍒紡螖 = b...
绛旓細F(鏃犵┓)=1, 鎵浠 d=1.X鏄繛缁殢鏈哄彉閲.F(x)涔熷繀椤绘槸杩炵画鐨.F(1)=0 --> F(1) = bxlnx+cx+d = bln1+c+d = c+1 = 0 --> c=-1 F(e)=1 --> F(e) = belne+c+d = be+(-1)+1 = be = 1 --> b=e^(-1)
绛旓細杩炵画鍨嬬殑闅忔満鍙橀噺鍙栧煎湪浠绘剰涓鐐圭殑姒傜巼閮芥槸0銆備綔涓烘帹璁猴紝杩炵画鍨嬮殢鏈哄彉閲忓湪鍖洪棿涓婂彇鍊肩殑姒傜巼涓庤繖涓尯闂存槸寮鍖洪棿杩樻槸闂尯闂存棤鍏炽傝娉ㄦ剰鐨勬槸锛屾鐜嘝{x=a}=0锛屼絾{X=a}骞朵笉鏄笉鍙兘浜嬩欢銆傚鏋滀竴涓嚱鏁板拰X鐨姒傜巼瀵嗗害鍑芥暟鍙栧间笉鍚岀殑鐐瑰彧鏈夋湁闄愪釜銆佸彲鏁版棤闄愪釜鎴栬呯浉瀵逛簬鏁翠釜瀹炴暟杞存潵璇存祴搴︿负0锛堟槸涓涓浂...
绛旓細閭e緢绠鍗曞晩锛屽亣濡傝浣犲湪涓嬪崍3:00宸﹀彸鍒拌揪鏁欏銆備綘纭垏鍒拌揪鐨勬椂闂村彲浠ョ湅鎴愭槸涓涓杩炵画闅忔満鍙橀噺鍚э紵閭d綘纭垏鍦3:05鍒嗗埌杈剧殑姒傜巼鏄灏戝憿锛熸槸0銆.涓轰粈涔堬紵浣犱笉绠℃庝箞鐪嬭〃瀵规椂闂达紝浣犳湁鐢熶箣骞翠笉鍙兘鍦ㄧ‘鍒囩殑3:05锛堢簿纭埌姣銆佸井濡欍佺撼绉掞紒锛夎笍鍏ユ暀瀹ゃ傜悊璁轰笂浣犺澶氬皯娆¢噸澶嶇粺璁℃墠鍙兘绮剧‘寰楀埌杩欎釜鐐瑰憿锛...
绛旓細X鏈嶄粠鍧囧寑鍒嗗竷,鍗砐~U(a,b),鍒橢(X)=(a+b)/2,D(X)=(b-a)²/12 璇佹槑濡備笅锛璁捐繛缁瀷闅忔満鍙橀噺X~U(a,b)閭d箞鍏跺垎甯冨嚱鏁癋(x)=(x-a)/(b-a),a鈮鈮 E(x)=鈭獸(x)dx=鈭(a鍒癰)(x-a)/(b-a)dx =(x²/2-a)/(b-a) |(a鍒癰)=(b²/2-a)/(b-a)...
绛旓細F(x)鏄垎甯冨嚱鏁帮紝鎵浠ュ彇鍊0鍒1涔嬮棿銆1锛 鑻<=0, 鍒 P{Y<y} =P{F(x)<y} = 0 2锛夎嫢0<y<1鏃讹紝P{Y<y} =P{F(x)<y} =P{X<F^-1 (y)}= F(F^-1 (y))=y,3锛夎嫢y>=1锛屽垯 P{Y<y} =P{F(x)<y} = P{F(x)<=1} = 1 鎵浠 Y 鏄痆0,1]鍖洪棿涓婄殑鍧囧寑鍒嗗竷...
绛旓細瑙佸浘
绛旓細=0.4 (3)銆佸F(X)姹傚灏卞彲浠ュ緱鍒X鐨瀵嗗害鍑芥暟f(X)锛屾墍浠 f(x) = 2x 0鈮<1 0 鍏朵粬 鎬ц川 闅忔満鍙橀噺鍦涓嶅悓鐨勬潯浠朵笅鐢变簬鍋剁劧鍥犵礌褰卞搷锛屽彲鑳藉彇鍚勭涓嶅悓鐨勫硷紝鏁呭叾鍏锋湁涓嶇‘瀹氭у拰闅忔満鎬э紝浣嗚繖浜涘彇鍊艰惤鍦ㄦ煇涓寖鍥寸殑姒傜巼鏄竴瀹氱殑锛屾绉嶅彉閲忕О涓洪殢鏈哄彉閲忋傞殢鏈哄彉閲忓彲浠ユ槸绂绘暎鍨嬬殑锛屼篃鍙互鏄繛缁...
绛旓細鏍规嵁鍙橀噺鐨勫彇鍊艰寖鍥达紝瀵硅仈鍚堟鐜囧瘑搴﹀嚱鏁扮Н鍒嗭紝瀵箉绉垎寰楀埌X鐨杈圭紭姒傜巼瀵嗗害锛屽x绉垎寰楀埌Y鐨勮竟缂樻鐜囧瘑搴﹁繃绋嬪涓嬶細