设二维随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]服从圆心在原点的单位圆内的均匀分布，求极坐标[tex=5.857x1.571]JOEsMCNmvUrPt9NFZFjvXdRScuFPWHk6n58offp7nI4=[/tex],[tex=11.071x1.357]yu4sTGcqfPs0xfoLD+/zWuYl/pL3OWHfy7AyetALdsDlUCYK7c6bcu7OkZfXfzvU[/tex]的联合密度函数.

2022-06-08

设二维随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]服从圆心在原点的单位圆内的均匀分布，求极坐标[tex=5.857x1.571]JOEsMCNmvUrPt9NFZFjvXdRScuFPWHk6n58offp7nI4=[/tex],[tex=11.071x1.357]yu4sTGcqfPs0xfoLD+/zWuYl/pL3OWHfy7AyetALdsDlUCYK7c6bcu7OkZfXfzvU[/tex]的联合密度函数.

答案：

解：二维随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的联合密度函数为[tex=15.071x4.071]A2h7jq+7ScMhJO/08ZwWHmjF+hPYwoIy7yyLTcmNy5FtwzuC/lECMnHWUqyyMFbJ7rsN3Bodfs3EwLO+aT3hBqAFpBf/6Pxql/wxGbjjAaQD6G6UCbDHffBiyNxvXMP3aAbE4gxxgBcMTFB48tZJT/1j/+ZQcRRUjkGwNJz0ggrfgBwcUaF3Hi82sgmdjky/[/tex]因[tex=7.143x4.214]7EJHVCtO2IWq3KpdB+jQsisgUIPx28iagsAsLG29AcifIMD8JZKE3Z65v5f3r0PLOI3cvEYf1zShtvqJpm1a6BdanIEvgj3d/W5x6E6l2jYoCgYgefxnzEeTkxd/qJKz[/tex]有反函数[tex=6.0x2.929]7EJHVCtO2IWq3KpdB+jQsvg/MWfujK/kgj3x0PyuHaZ4k5AiBz4DwzalqtTK3NaDIJLS+eBTr7gVT3RmwIZBl6TXJliRT7vQRCk04a3ILDU=[/tex]且[tex=16.5x3.357]oD5iFPok0DMpNoHwEGueewsDio/BqBarr6evcilPa0WmacEhD8HRfB0sGthjNFXLLMVFZqymdsw7rU53s2nyU8so4be5++D8FrOezQHYl7PoGAioi3LFHe598oDsifDoAzquKP8KGT17YKMAgKJW76PVRbW7jjc1mFlYp9NJcT7gd0GYj9SWZ2sGY2/n8+3YbK5HeNvTfYgz8/YTfmahx6jSVkvMNK1SC4PsrJBQTjpcU7X2boHxN2Cgu3YPmlO5P5oRZJUlKl8n5H+lb7cRGRjWJ90ixGqlFHQqzeYwCRO1ibv4SZc83QQCzvqDZur8[/tex]且当 [tex=6.357x1.429]ANwvtYxbz3CSbp8A/lEzZqkLImKLIS622NpaIdyNeT4=[/tex]时，有 [tex=10.429x1.214]1KIY9uEVM5fU3NMnKa+48uZgfyAZfgLtflKAHLUvmCYr9gjGuIRfvJHKZm6n3afl[/tex]故[tex=2.286x1.357]kAhe6OucELBYmdUfvu53ow==[/tex]的联合密度函数为[tex=27.5x3.929]9PCYacLiTR/n2x51n5OOyqQAzOeQMS1c/ZxmSFYhGTGwpGcTz3wGVQsZdcPuEp9IlsivVeZUEof4u3V1cwSQIwJGjQFh7ObTqDX2N7KfH609P956r1s3t2RrucJ2BNRhhT5b5qiLNwRq8OTH+a90KpPaiEwAefts9CUVhv+BBZekbXioB6R0VLGSeKHl9quz5diI+4yloujgQo97gAmFpkHq19r0lAHQulWuCo4l37nDJpjkpUIOkKu4QF2vy6sJBozhjo2zWVWevJaUhOyTfw==[/tex]

举一反三

内容

0
设二维随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的联合密度函数为[tex=12.143x2.429]s59y2K1bDNChzmHwfrn1oe9Qe7QX3DfOdcblC8X55/FFjEIpK5VeKXJ/Cik2hBKZ08SdcK2DK5UnfFEY/m9/LNGcnWAYrng+I9AKYq7dxGw=[/tex]试求[tex=5.714x1.357]wEkbknub4MAE0LxiOE6rbg==[/tex].[img=224x197]177dc88ffa326d8.png[/img]
1
设二维随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的联合密度函数如下，试问[tex=2.643x1.286]1Hu3J6L7ix9b4TuPkzZg9w==[/tex]是否相互独立？[tex=13.5x2.929]k577xRm0ZOCUJhn0k/ylevdeQMRjBzLLf+gr+H41+NBM4P2PL1RUz/igQU9VyZ3MEv6oxwe67pVfh9T4JZXFsntMtIzZFhDyThno+s0oGhjVCF9aTUJtxUJAD7IIns1V[/tex]
2
设二维离散随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex]的联合分布列为[img=347x260]177e690b09433a7.png[/img]试求[tex=5.071x1.357]aLi00BfMGa6v+kENQ3ABmw==[/tex]和 [tex=5.071x1.357]lWiOdgh0KWDvXy0zBDkOXg==[/tex].
3
设随机变量(X,Y)的概率分布列为[img=345x154]178ab1c9ce3bc1b.png[/img]求[tex=1.571x1.0]JUrGU6ftUjxQCIr6CyfDwQ==[/tex],[tex=1.357x1.0]yL/7/hhyqgwzAX8jnIq3OQ==[/tex],[tex=4.357x1.357]LN0xwhQHSOeLwBClUlpHQw==[/tex].
4
设随机变量[tex=2.5x1.357]PWg5V4GQQafckGNgbx6gmw==[/tex] 的联合密度函数为[tex=15.714x3.357]gW4ZfOZceOP4na2kefvCNkrTiJsylrgC4FiT/ATmIksLlXpjKIN/4BAal0ecfy1HmX8nfYJHHJSNO8rhoRlgGgoXTf7S73BJDxHMzMKXz3X6oQc7FJSDdVsIxBx6ELUAKCyZpo1xD64GpEAAiaRRMw==[/tex]试求边际密度函数[tex=5.5x1.286]DjMU0sN9p3UeEMImNPuGD5eBRs7CEsoklO2WxY5fTcs=[/tex].[img=243x153]177dd38c1bd4eda.png[/img]