• 2022-06-08
    设二维随机变量 [tex=2.786x1.286]wsm6hZKLwoHLmpiSvjoPLA==[/tex]  服从区域  [tex=10.929x1.286]bf7mxN/1XbjV+1U5hRGMJUfk2UVQmDuhsNzlbsabcB65aewQwXq9VbU3MC7M2ndw[/tex]  上的均匀分布,求:(1)  [tex=2.786x1.286]rHpbFIkzEXdrQ+mcZyCBkQ==[/tex]  条件下  [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]  的条件密度函数.(2) [tex=2.643x1.286]T0WCDggc1xWksEhYC1fmtA==[/tex]  条件下  [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]  的条件密度函数.
  • 解 根据区域  [tex=10.929x1.286]bf7mxN/1XbjV+1U5hRGMJUfk2UVQmDuhsNzlbsabcB65aewQwXq9VbU3MC7M2ndw[/tex]  的面积[tex=18.786x2.429]SxxaBszjGdnF6xnZPM56AxOeO9/aEESVZAz8dh9G1C+VbpIZFjpjpI0fxohAc28hZKq9U/pywoomi2jHnoxk5phPY7M54xSPpIGL3Y8ab4Ai88AoLJ25v6DFCfG4DHAHHjS+iJfnz3Jn0tLavgFnUQ==[/tex]可知 [tex=2.786x1.286]wsm6hZKLwoHLmpiSvjoPLA==[/tex]  的联合密度函数为[p=align:center][tex=11.429x3.643]lJblPB9MNpIrc6Sy3BdmFT9prTUl96wVR97mrT005OP3HXzm8ecSkS2Yka/6840vOZ51+9wapUozuHa6IK0FjxW9tUqYkZ4tiXiKV1opBL0=[/tex]由此求得(1) [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]的边缘密度函数为[p=align:center] [tex=21.857x6.357]7Kck5/+xhjQcWS3X0M1SfryiRG+4QY+MZV2BXjKJzxHIblYmgZyHp1rssvRLevAa8C8suJ9G/oKQsQP2TYIcY5Kv10piLe0wBNri6bWPPTnVODiZ3EcoQqcHNfV7LvoPTcQbDTTcUBggqOwYXfc3Z15XLfKCh9woi5jhRMqJrXbmNRrDVkWO0DJBupdwrRzwuMM9ryyr/a12ZEBoXdLtfMMXNC4tkpItdXvUNZWeg7sJGrVZPqOZrYUVf6ykgDWZaDAM7ywAfn3FZ7mzWS7TkYpyLdtVzrs7MuXRcx/h/dg=[/tex]故 [tex=2.786x1.286]rHpbFIkzEXdrQ+mcZyCBkQ==[/tex]  条件下  [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]  的条件密度函数为[p=align:center][tex=17.5x3.643]fPRNjA1zxkI/9b+mS1LBWvITwh/jDN5nELEs4NW7jdX6ZhtsKKkl7QCoqlmHvq744kfX0GafIaw/ZHa9sBN7wXAJyTaTI9fR96qAst90TulWytnUsuZzKLJ8sZpUcoRwvoNjI8haOlAb4srf9oIEFUlZ0TnQGLUysfWJ6LsaT6s=[/tex](2)[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]的边缘密度函数为[p=align:center][tex=32.571x3.929]DyHW+/Px+wb1h8q20bT96b4M3uXf4wvK8iHEY9VXDC/qvb3STpWXM98Een+nQlJaMe4f8769/kzAwDQ4YDWfTp8ROZ8mMoSsN4lH8O77e0q+tzMYr7ymvAq9Fw3HPzs0z0ua41bEtA7pJq8C3/uydhVBysnCxw2tTHGGSBIlI9fnqliDbvJxBgwO6ZGzPcermxGy0jnLw3ro8ppXnd0lwuInC4Z4XP46azeDAG+h7oERypxK6lEqRSvjAkll0ih89rKNhO2obEkAdboV12K2DA==[/tex]故  [tex=2.643x1.286]T0WCDggc1xWksEhYC1fmtA==[/tex] 条件下  [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]  的条件密度函数为[tex=18.071x3.857]rYG2S515UwCNaBU2GlXQUSfNlpa51mLaeCxxhgjrZ0OZuLA3FJRqGSd2NhU+ZozKIZRDeQotQUkRnp2rrGDv/yoQN4Py/OAs125BsJIC9LEJ3krcKdfGZxPcJu2WdtYMxeT5FycGKhnLZrxP3H6/OQy/GKLTTztwNJrZ7j8+DP0=[/tex]为直观起见,其中条件 [tex=4.643x1.286]LVK91zCuvT9Ef3AxIyjOTA==[/tex]  等价表示为  [tex=5.071x1.286]t9BWM+LByOgTBj5N9nPg4x3Ct4oZ25dUp3jn3FGJiPw=[/tex] . 

    举一反三

    内容

    • 0

      设随机变量[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]服从区间[tex=1.929x1.286]iMAZ+4hDYSeldsmK7BlytA==[/tex]上的均匀分布,[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]服从[tex=2.357x1.286]AXVYg5COGe7fG0Iatqkkig==[/tex]的指数分布,且[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex],[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]相互独立,则[tex=2.786x1.286]AG5D6gU/evQZlfwisXgzYw==[/tex]的联合密度函数[input=type:blank,size:4][/input]。

    • 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

      设随机变量 [tex=2.071x1.286]AABPNNktZOJp9yYomaK2LQ==[/tex] 相互独立,若 [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex] 服从[tex=2.786x1.286]/KEynkd+g4g8yS0qXSk9mg==[/tex] 上的均匀分布,[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 服从参数为 1 的指数分布,求随机变量 [tex=3.714x1.143]wQlTAdtDs1fa21EP7mnykg==[/tex] 的概率密度.

    • 3

      设随机变量  [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]  与  [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]  相互独立,  [tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]  服从正态分布  [tex=3.929x1.286]N5dq4BwkTdWMAb0OmXWoEaQHcjMspfC0l4+u6bRl6uAvEVUQUcSxPV1hL5aXeKrf[/tex], [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]  服从均匀分布 [tex=3.857x1.286]oINv2OUrkfWf54e8Ht2lD1iv2R1pi2JiMcP1OIfioeI=[/tex] , 求  [tex=4.929x1.286]bstb6Acm/GnARrPc8f1uPw==[/tex]  的密度函数.

    • 4

      设随机变量[tex=0.929x1.286]uswT/CEcOIwMpCvTz/zeaA==[/tex]服从区间[tex=2.143x1.286]l9DYubvhJSmV7cTo/ad4fA==[/tex]上得均匀分布,(1)求[tex=3.357x1.286]s8MxvfWC9l8tAzB+vk6hQg==[/tex]得密度函数;(2)[tex=4.286x1.286]f4K1gTBjsCQR6d//JYB5/A==[/tex] .