举一反三
- 设以下所涉及的数学期望均存在，试证:[tex=12.5x1.357]+OyS9GR+P0Hab3whhf5YkY7XV4YukPC0ntEUDlh5eoEN7mmDHSTqZQmGcf61O2g3[/tex].
- 设随机变量[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]的概率密度为[tex=8.071x1.5]T+swXBVehuKEGcHkJEQha0A2yOB+gXV0a45pPyAYLDBW3ad7NANF4nW5pzFdZVAX[/tex].试求：（1）[tex=3.214x1.214]/QdchUsMZt66wWdpI6z6mw==[/tex]的数学期望.（2）[tex=3.357x1.214]oEoE1f2QGbzZifhTqwZVQV0oaktUYH/gQNTRui20i+0=[/tex]的数学期望.
- 设[tex=3.143x1.214]MmeklMP/j6saWqycN/i3Z/a69BxU/XzAAmVLUDwLAKYsGROs6hwqumtrrypVwJLZ[/tex]是 [tex=2.429x1.071]kaIcCzgC6SpeVVzRje1dYA==[/tex] 方阵[tex=5.786x1.214]uSJxMvQZ0VWTKkbNd1sz3Q==[/tex]试证如果[tex=9.857x1.357]KNz1FY9OAxkHJ6m0crUOlLQnAzLePqaEkKGo26MdANc=[/tex]则[tex=12.5x1.357]j1UW3kvoxPwU8IkDv6BF1SHztaQn6enIK4q8bKGDloHemP5HRVc3eNHhd4woEIvDIvuc6phH6qy9P2F6L/fvpQLm96yU+JQuEYsY3bG3E3dHzUBojYCTzotgWbwyzLLPj4wbQCYUoB7GMqhgm7Hli1Zpc08vZa3rB/3FFf4H+NnLwlFAA5mB2/6FIASxpxyh[/tex]并计算 [tex=4.286x1.143]Rt43yfj/R7vZbskTbnkKRYw4Bhs7CQqPUDVH0KrKY0rpESjCsltPX9XuAUmcYzd4[/tex]
- 设 [tex=9.857x1.357]0T+1c7zq/idbMqaaWgotqWHr6fZNYBkXTLjhyQglJzp0iOIdZEz3WbEw/Pb+3qlO[/tex] 又 [tex=1.857x1.357]VHvV9DduV1/OkZRTTw1+mg==[/tex] 满足 [p=align:center][tex=6.357x1.357]+3zmuKty1AhSMDB3tNdbXxLJRZTFKVq4xUmyZwpiyJg=[/tex]，则 [tex=4.571x1.357]NaXhQuud9whTIdEia7cAy145H6cmmDHeiC85YWZqPkg=[/tex] 或 [tex=4.571x1.357]yOyH9WGEdakx47yTMUJ/qAG7LUpVFYIOzNODeDvbQnM=[/tex].试证 [tex=1.857x1.357]VHvV9DduV1/OkZRTTw1+mg==[/tex] 不可约.
- X, Y, Z 为 3 个随机变量, 证明以下不等式成立并指出等号成立的条件。[br][/br][tex=9.857x1.357]NUQqMUcZfsYXZe7a52OqVASX+mUkVagLNw3xFgiaXiIiYkJHYirg7FRWhFIaD68w[/tex][br][/br]
内容
- 0
设随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex] 的联合分布列为[tex=8.286x4.929]I08GkjPu5ilZ1cL3oVOjRE4sVTHAWb1Gvi9jJxpOnvgQGFRJYElTp76dCQHNW2EiJToy5XVFxu0JSBlgCu3B1uXbj6iYf+TOajaf/f9UGxe7277AvLT+uoSg/2eSnzT1hTwgxRixvf/blDxkqAeW2Hw1UzwR8F4aogEZBoPniOU=[/tex]试求[tex=7.929x2.214]hXf55bRVod3Y9t5SvIsmdH2BcILqGCkA66a7tQ+JJ49GVS4Sw9PkqI4AwRREqVxM[/tex]的数学期望.
- 1
设随机变量X与Y相互独立，且均服从N(0,1)，试证[tex=4.5x1.429]VAArUfNzfswx5txbgwZKkg==[/tex]与[tex=3.214x1.357]nsf0G17h4jB8nprD/RsLtA==[/tex]是相互独立的随机变量。
- 2
设随机变量[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]的数学期望[tex=1.714x1.286]p+zOLBbKURbVjWbmuQcavg==[/tex]和方差[tex=3.5x1.286]12sUUDPHdI8B5whH1oKOEg==[/tex]都存在，令[tex=9.643x1.286]q8rx/C91kAwHquavAAmThTm1Da+jO6MCodG7xN4wd4o=[/tex]，则[tex=2.643x1.286]W5dZvAEYle8EUftPQgDsQA==[/tex][input=type:blank,size:4][/input]。
- 3
设随机变量[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]和[tex=0.643x1.0]O+viFNA0oHTwnBtQyi80Zw==[/tex]的数学期望分别为–2，2，方差分别为1和4，而相关系数为-0.5，试根据切比雪夫不等式估计概率[tex=6.0x1.357]VX6yEWKc64r7q+Z+DWQGYg==[/tex].
- 4
设 [tex=16.643x2.714]V1D753We7vezsBlKQyfrUpu5fHehILnpclZBTX9G5qYh2VPrlUOM2wtJerhh3oeoUfI5nmoWiznyOTLrs+NBs7M1QYvA3ki0EjY8m+qU3zOJHuL3oJ+HYiLfHFrWUhNe[/tex]. 试证存在 [tex=4.214x1.357]jxvhZiY+yy3z8BpZfEQInA==[/tex] 满足 [tex=23.643x2.714]V1D753We7vezsBlKQyfrUnVAmoUVjD6x2LgzfiEY/Dfd4ygmAkWq6o2VtzMBisOMpny8Cm6rwgEElFfVvOzrWisahcWlCLOyDEE8bnVzb7G6f285T7wImS6H1Fw5BNipbeII+6meqi+CqSss3aPyA6Xb1g//h3TCehjRrEouP3PZfY2W2lBBi0KWawpIbs2V[/tex]，使得 [tex=13.714x1.357]JNlAoK3ZaT13qtKkGDLOCh79MhHpxEc4+TV1E+mpOzqmBS/pbUkmdFEGB2ednNel[/tex].