设随机变量[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]，[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]，[tex=0.786x1.286]YmC97Clv6J6k2IyNV61eAw==[/tex]满足[tex=6.286x1.286]mJnBMUbSik+EXYpyNJ3LCg==[/tex]，[tex=4.786x1.286]Ngq15F4EZSjXtVhJtA3pGQ==[/tex]，[tex=10.0x1.286]I9y++zSKq8ldcXFIXumc8xu3teEDlSRgqvI5OYMrxBw=[/tex]，[tex=3.643x1.286]lYJmJoJzCSlC8Okk2jEfgLZHNcEyO7r2iUY4NYQugu0=[/tex]，[tex=7.571x2.0]SP+U6tD7a7vs5yxw6/64hhv4e5P8OQkbbYTGW+qzl5quPgayHZeqtZyCxGbyduft[/tex]。试求：[tex=6.286x1.286]u+VKZGJz9dS6yMwLXX7FoA==[/tex]，[tex=6.286x1.286]gLGhVa79tNFEjuPkbDnRpg==[/tex]。

2022-11-01

设随机变量[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]，[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]，[tex=0.786x1.286]YmC97Clv6J6k2IyNV61eAw==[/tex]满足[tex=6.286x1.286]mJnBMUbSik+EXYpyNJ3LCg==[/tex]，[tex=4.786x1.286]Ngq15F4EZSjXtVhJtA3pGQ==[/tex]，[tex=10.0x1.286]I9y++zSKq8ldcXFIXumc8xu3teEDlSRgqvI5OYMrxBw=[/tex]，[tex=3.643x1.286]lYJmJoJzCSlC8Okk2jEfgLZHNcEyO7r2iUY4NYQugu0=[/tex]，[tex=7.571x2.0]SP+U6tD7a7vs5yxw6/64hhv4e5P8OQkbbYTGW+qzl5quPgayHZeqtZyCxGbyduft[/tex]。试求：[tex=6.286x1.286]u+VKZGJz9dS6yMwLXX7FoA==[/tex]，[tex=6.286x1.286]gLGhVa79tNFEjuPkbDnRpg==[/tex]。

答案：

按数学期望、方差的性质：[tex=14.714x1.286]JHERJiYvqcuF0oUpuwLdz4ujd9pCB8hEFvvXsGG3b2s=[/tex]，[tex=15.643x1.286]yZKomXZfpdW5mUtSzbKiKUak9R+Bo7LPJDug1XLfTiI=[/tex][tex=15.714x1.286]ZbU6Ks4tYWr78J/300Im+k4JUYhacFUfOSQCkG6v2/wCml2OQDChinZdRXkiMZpVw10j6AlATGswRAfyeY5bOw==[/tex]以及[tex=12.286x1.286]s/tPbxkoMXAUnNv0r5j7kK80Lg6nkGrxduI8cwrduKO7FNrvzJ9c/+26JNErYeuM735I53DV30NIa/jcnW42GQ==[/tex]计算[tex=6.286x1.286]u+VKZGJz9dS6yMwLXX7FoA==[/tex]和[tex=6.286x1.286]gLGhVa79tNFEjuPkbDnRpg==[/tex]。解：[tex=16.429x1.286]JHERJiYvqcuF0oUpuwLdz8Yrd3EutdHasLyHctl/UuM=[/tex]；[tex=39.857x5.643]mmCRP+Vrds8djtenrMyMWxMoNPMNwTzTeBQIeM+hfzY2slO5bfmom8T5UJnURsinr7pHaaDuVWHwgbuhHBgCnfHfB7t5puzM++zoQRShmvnJgnekbFmRl/Pk7VEVOcwgaHlv04+kNlfEot1n1WJGCwkB2TPGKmezkBeyKanoV4FMk+eUtFGu1vSDukO9kTNC4esE1bHsRcB6nfCJWVyeds+bZXhROzdJ+NP55k4w5nv9UoO9Mivofmu7cp/mSbOp6/wODYQesiPwpjPJzk4tTkja+okc4ZGzshJqxys7nC2Dw+2TP28Aj0KJK31Os1FoYBbXoAsYTWmCkbRWO8RK8eiRWlfF1z31hRP7F1f3d1Qblh6q+NX4dQtSjno3vzT/CnSRND8ArvGw5rsYaM3gFLZLi/+rT6XS9JaAa5S9U5xOuhH7Ypw5Jc+yUV2BLCYVKlLYGis9OCM6HPZDWn62aA==[/tex]

举一反三

内容

0
设随机变量[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]和[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]都服从[tex=2.143x1.286]dboSCjP3Fn5+xkkJFCNE+A==[/tex]分布，证明： “[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]和[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]不相关”与“[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]和[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]独立”等价．
1
设[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]和[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]是两个相互独立的随机变量，[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]在[tex=2.929x1.286]kvrkODQf0L3CKREOEdSkuA==[/tex]上服从均匀分布，[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]的概率密度为[tex=10.571x2.429]DRJq+C1mHjswrEZ8FtvX7HNGAPrBLJ6gzRGG2ilTN7MM55jZEydQmT0AUl0Qb5hAT5k9ols3J/KpgflWFdX4TQ==[/tex]，求：（1）[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]和[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]的联合概率密度；（2）[tex=4.714x1.286]dbgFLPFxgdKKXnbc/gnthjs3iie6rgn/UEwrXH27vHI=[/tex] .
2
设X和Y是两个拓扑空间，[tex=4.786x1.286]YTQzLz+sesI1dQ5UGt8Nb7XN1gDRtIK2HjDLwQB/utY=[/tex]是连续映射，证明：如果[tex=0.786x1.286]YmC97Clv6J6k2IyNV61eAw==[/tex]是[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]的一个连通子集，则[tex=2.143x1.286]lYyNPJbhUCYK1wTeekhvmA==[/tex]是Y的一个连通子集。
3
判断下列命题是否为真：（1）[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex]（2）[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex]（3）[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex]（4）[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex]（5）[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex]（6）[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex]（7）若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex]，则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex]（8）若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex]，则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]
4
设二维随机变量[tex=2.786x1.286]vzGOG+JNlRurOKCm31T4Kw==[/tex]在圆域[tex=5.357x1.286]oOYTzm/NiJqJo4OjC55er1L5z17HiYuK5dHQrlDB2IM=[/tex]上服从均匀分布，（1）求[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]和[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]的相关系数[tex=0.571x1.286]mGHbklYlBVNXKEGAelwITA==[/tex]；（2）问[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]，[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]是否独立？