设以下所涉及的数学期望均存在，试证:[tex=9.857x1.357]FtaN909HufsxEh4cU6OHrMeayzCdlo3V3XHbgBUeJlc=[/tex].
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]