设X服从（0,5）上的均匀分布，则P｛2≤X≤4｝= 设（X，Y）服从平面上圆域x2+y2≤4上的均匀分布，则P{...
\u8bbeX\u670d\u4ece\uff080,5\uff09\u4e0a\u7684\u5747\u5300\u5206\u5e03\uff0c\u5219P\uff5b2\u2264X\u22644\uff5d=_____,P={4\u2264X\u22646}=_____? \u8bf7\u5199\u51fa\u5177\u4f53\u8fc7\u7a0b\uff0c\u8c22\u8c22P\uff5b2\u2264X\u22644\uff5d=_0.4____,P={4\u2264duX\u22646}=__0.2___
\u9996\u5148\u6982\u7387\u5bc6\u5ea6\u57280\u52305\u4e0a\u662f1/5\uff0c\u5728\u8303\u56f4\u4e4b\u5916\u4e3a0P\uff5b2\u2264X\u22644\uff5d\u7b49\u4e8e1/5\u57282\u52304\u4e0a\u79ef\u5206
P={4\u2264X\u22646\uff5d\u7b49\u4e8e1/5\u57284\u52305\u4e0a\u79ef\u5206\u52a0\u4e0a0\u57285\u52306\u8303\u56f4\u79ef\u5206
\u4f8b\u5982\uff1a
\u968f\u673a\u53d8\u91cfX\u670d\u4ece\u533a\u95f4[0,5]\u4e0a\u7684\u5747\u5300\u5206\u5e03 ---> f(x)=1/5, 0<x<5
2X+4\u226410 --> X\u22643
\u6240\u4ee5\uff0cP{2X+4\u226410} = P(X\u22643) = (3)(1/5) = 3/5
\u6269\u5c55\u8d44\u6599\uff1a
\u5355\u7eaf\u7684\u8bb2\u6982\u7387\u5bc6\u5ea6\u6ca1\u6709\u5b9e\u9645\u7684\u610f\u4e49\uff0c\u5b83\u5fc5\u987b\u6709\u786e\u5b9a\u7684\u6709\u754c\u533a\u95f4\u4e3a\u524d\u63d0\u3002\u53ef\u4ee5\u628a\u6982\u7387\u5bc6\u5ea6\u770b\u6210\u662f\u7eb5\u5750\u6807\uff0c\u533a\u95f4\u770b\u6210\u662f\u6a2a\u5750\u6807\uff0c\u6982\u7387\u5bc6\u5ea6\u5bf9\u533a\u95f4\u7684\u79ef\u5206\u5c31\u662f\u9762\u79ef\uff0c\u800c\u8fd9\u4e2a\u9762\u79ef\u5c31\u662f\u4e8b\u4ef6\u5728\u8fd9\u4e2a\u533a\u95f4\u53d1\u751f\u7684\u6982\u7387\uff0c\u6240\u6709\u9762\u79ef\u7684\u548c\u4e3a1\u3002\u6240\u4ee5\u5355\u72ec\u5206\u6790\u4e00\u4e2a\u70b9\u7684\u6982\u7387\u5bc6\u5ea6\u662f\u6ca1\u6709\u4efb\u4f55\u610f\u4e49\u7684\uff0c\u5b83\u5fc5\u987b\u8981\u6709\u533a\u95f4\u4f5c\u4e3a\u53c2\u8003\u548c\u5bf9\u6bd4\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u6982\u7387\u5bc6\u5ea6
\u5982\u56fe\u6240\u793a\uff0c\u9898\u5e72\u4e2d\u5706\u4e3ax2+y2\u22644\uff0c\u56fe\u4e2d\u9634\u5f71\u90e8\u5206\u4e3a\u5728\u6b64\u5706\u5185\u6ee1\u8db3\u6761\u4ef6X\uff1cY\u7684\u90e8\u5206\uff0e\u6240\u4ee5\u6839\u636e\u51e0\u4f55\u6982\u578b\u53ef\u5f97P{X\uff1cY}=S\u9634\u5f71\u90e8\u5206Sx2+y2\u22644\uff1d2\u03c04\u03c0\uff1d12\u6545\u7b54\u6848\u9009D
P｛2≤X≤4｝=_0.4____,P={4≤X≤6}=__0.2___
首先概率密度在
0到5上是
1/5
，在范围之外为0
P｛2≤X≤4｝
等于1/5在
2到4上积分
P={4≤X≤6｝等于1/5在
4到5上积分
加上
0在5到6范围积分
随机变量x服从区间[0,5]上的均匀分布
--->
f(x)=1/5,
0
x≤3
所以,
p{2x+4≤10}
=
p(x≤3)
=
(3)(1/5)
=
3/5
绛旓細棣栧厛姒傜巼瀵嗗害鍦0鍒5涓婃槸1/5锛屽湪鑼冨洿涔嬪涓0P锝2鈮鈮4锝濈瓑浜1/5鍦2鍒4涓婄Н鍒 P={4鈮鈮6锝濈瓑浜1/5鍦4鍒5涓婄Н鍒嗗姞涓0鍦5鍒6鑼冨洿绉垎 渚嬪锛氶殢鏈哄彉閲X鏈嶄粠鍖洪棿[0,5]涓婄殑鍧囧寑鍒嗗竷 ---> f(x)=1/5, 0<x<5 2X+4鈮10 --> X鈮3 鎵浠ワ紝P{2X+4鈮10} = P(X鈮3) = (3)(...
绛旓細0鍒5涓婃槸 1/5 锛鍦ㄨ寖鍥翠箣澶栦负0 P锝2鈮X鈮4锝 绛変簬1/5鍦 2鍒4涓婄Н鍒 P={4鈮鈮6锝濈瓑浜1/5鍦 4鍒5涓婄Н鍒 鍔犱笂 0鍦5鍒6鑼冨洿绉垎
绛旓細鑰岋紝X銆乊鐩镐簰鐙珛锛屸埓(X,Y)鐨勫瘑搴﹀嚱鏁癴(x,y)=f(x)*f(y)=e^(-5y)锛寈鈭(0,5)銆亂鈭(0,鈭)銆乫(x,y)=0锛寈∉(0,5)銆亂∉(0,鈭)銆備緵鍙傝冦
绛旓細P{X鈮3}=F(3)=(3-0)/(5-0)=3/5
绛旓細璁＄畻杩囩▼濡備笅锛氭牴鎹鎰忓彲鐭 鏂圭▼4x^2+4Xx+X+2=0鐨勪袱涓牴瀹炴牴閮芥槸瀹炴牴 鎵浠モ柍=4X*4X-4*4锛圶+2锛>=0 X>=2鎴朮<=-1 鍥犱负X鍦锛0锛5锛変笂鏈嶄粠鍧囧寑鍒嗗竷 鎵浠灞炰簬[2锛5)鎵浠ヤ袱涓牴瀹炴牴閮芥槸瀹炴牴鐨勬鐜嘝=锛5-2锛/锛5-0锛=3/5 ...
绛旓細锛4X锛塣2-4*a(X+2)>=0 寰楀埌X>=2鎴朮<=-1 鑰0<X<5 寰楀埌2<=X<5 闅忔満鍙橀噺X鍦锛0锛5锛変笂鏈嶄粠鍧囧寑鍒嗗竷 鎵浠=锛5-2锛/锛5-0锛=0.6
绛旓細未=x^2-4>=0 瑙ｅ緱x>2鎴<-2 闅忔満鍙橀噺X鏈嶄粠鍖洪棿銆1,5銆涓婄殑鍧囧寑鍒嗗竷 浠庤屾柟绋嬫湁瀹炴牴鐨勬鐜嘝=锛5-2锛/锛5-1锛=0.75 渚嬪锛氭柟绋媥2+2Yx+1=0鏈夊疄鏍 鍒欌柍=锛2Y锛塪u²-4=4Y²-4鈮0 瑙ｅ緱Y鈮1鎴朰鈮-1 鍙圷鈭锛0,5锛鎵浠鈮1鐨勬鐜囦负锛5-1锛/5=4/5 鏁呮柟绋媥2+2...
绛旓細瑙ｏ細P(X<=1/2)=1/4 Y~(3,1/4)P(Y=1)=C(3,1)1/4*(3/4)^2=27/64 濡傛湁鎰忚锛屾杩庤璁猴紝鍏卞悓瀛︿範锛涘鏈夊府鍔╋紝璇烽変负婊℃剰鍥炵瓟锛
绛旓細0.52x+锛118-x锛*0.33=53
绛旓細鏂圭▼鏈夊疄鏍癸紝鎵浠16K^2-4(4(K+2))>=0 鍖栫畝锛孠^2-K-2>=0 鍗(K-2)(K+1)>=0 鍗矺>2鎴朘<-1鏃讹紝鏂圭▼鏈夊疄鏍 鍥犱负K~U锛0,5锛鎵浠0<K<5 鎵浠=3/5
