试证明下列命题：设 [tex=7.214x1.214]Id1KXDgy9AwhlHPP3PITg3UiPIaEomyf6GGfVSFHoMw=[/tex], 若 [tex=7.0x1.357]t5/sj0lDmJGpbEiigtWR01XqwVVYLVPEYw265xyiDthwkwFjJpYh7O2dFlKb1toR[/tex], 则对 [tex=4.143x1.214]a9nr5iViflqlzU0IeJZaIA==[/tex],有 [tex=6.5x1.357]2eRelOVMOIHpBCNBXaPOV91GdHqKN8vb+sQCXAUubuY=[/tex].
举一反三
- 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]
- 设[tex=3.857x1.214]uccIuh12mnx73S5Ln9Nunw==[/tex]是一个格，试证明对于任意的元素[tex=4.214x1.214]Y06Z1LJtCprXckc80W0iZA==[/tex], 有下列命题成立:(1) 若 [tex=4.5x1.0]WcE2DLqIV0cG66Vf85rLlKJbDQNOs9fDIkf6U7t4ilE=[/tex], 则[tex=1.786x1.0]e6yz2KDSejyMapjVGIIQDA==[/tex](2) 若[tex=7.143x1.0]8RU1lANXRSMHjwx54SAdQAXSeXnRR6q5vEh8fR/Xnayn8vpdo6nmOCmalJO3ZqOH[/tex], 则[tex=3.0x1.0]qqnT8KQ4H6PBzTvMNo6gSg==[/tex](3)[tex=15.714x1.357]7T0Bbj2YX1smDBDQBkyV0PkjcnhM1np3rkLbY+fP5ciJJrKr+23uGRRGEVpgvz9GZpNF0IL6BH13upU9VC8DRF2K4OSZUgZuaaV8kpzIBUo=[/tex]
- 设二维离散随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的可能值为(0, 0)，(−1, 1)，(−1, 2)，(1, 0)，且取这些值的概率依次为1/6, 1/3, 1/12, 5/12，试求[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]与[tex=0.643x1.0]O+viFNA0oHTwnBtQyi80Zw==[/tex] 各自的边际分布列．
- 设 [tex=4.071x1.286]nR/cJv6OqBZsTDNk+MpaBw==[/tex]，证明不等式[p=align:center][tex=12.0x2.286]X/Ri20XB58Oz2ZfZYw8yP6qEPtmDovjJXhp8eOv8KNGfaJgnC6X1XEJ+2xzOJGQkwqKgHtAAyzdujVIOGdlO7gycABMU66WddDs30mp1D7k=[/tex]。（本题满分8分）
- 证明：设[tex=2.5x1.143]TiKXNJpck7QZybOVpHjBBQ==[/tex]，则(1)[tex=4.071x1.357]XuP7RmUEJaAkHVU8iAv+9Q==[/tex]；(2)[tex=4.214x1.357]AqKFQ399rus+wrghQrqZ2w==[/tex]；(3)[tex=6.714x1.5]88w0pH97sf309OJM2l0ulfXdE4LOhDA5RyW64p7MDoY=[/tex]。[br][/br]