第三章習(xí)題答案 二維隨機(jī)變量及其概率分布(1)

1、第三章第三章二維隨機(jī)變量及其概率分布二維隨機(jī)變量及其概率分布習(xí)題一習(xí)題一一、（1）于任意實(shí)數(shù)，有；yx1)(0??yxF(2)對(duì)分別是單調(diào)不減的；)(yxFyx(3)對(duì)于任意實(shí)數(shù)有0yx???)(yF???xlim?)(yxF=0)(??xF???ylim?)(yxF01?????)(F??????yxlim?)(yxF?????)(F??????yxlim?)(yxF(4)對(duì)任意分別是右連續(xù)的；)(yxFyx（5）對(duì)任意有2121yy

2、xx??0)()()()(11122122????yxFyxFyxFyxF二、)()()()(??????????xFYxXPxXPxFX????ylim)(yxF)()()()(yFyYXPxYPxFY??????????????xlim)(yxF習(xí)題二習(xí)題二一、?0123P025025025025?012345P003009015021024028隨機(jī)變量不獨(dú)立??與二、解：的取值為1，2，3，的取值為2，3，4，故的聯(lián)合分布率為X

3、Y)(YXYX234.iP123161616016160016121316???????????000arctan2)()(yyyyFyFY?三、解：（1），??????????????001)(lim)()(5.0其它xeyxFxFxFxyX???????其它001)(5.0yeyFyY（2）????????????其它00025.0)()(5.02yxeyxFyxpyx而????????????其它005.0)()(5.0xedyy

4、xpxpxX或????????其它005.0)()(5.0yeyFypyYY（3）???????????1.01.01.0)()1.01.0(edxdyyxpYXP四、解：（1）區(qū)域的面積為D?????2034202)(xxdxdyDS從而?????????其它02020)(243xxyxyxp（2），???????????????????????其其其其020)2(02043)()(243202xxxxdydyyxpxpxxX????