设[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]与[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]相互独立,已知[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]服从[tex=2.143x1.286]VykF7BpO3NFT550xU7Tx1w==[/tex]上的均匀分布, [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]服入指数分布[tex=1.786x1.357]NAcaUWG0M+fOpH6/Gh1yyQ==[/tex] .试求[tex=6.643x1.357]y80Y546TKJ9w+MUm0oMHBg==[/tex],[tex=6.286x1.357]k/hzUMjV7geOFY7iA5ZJqQ==[/tex]的概率密度.

2022-06-09

设[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]与[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]相互独立,已知[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]服从[tex=2.143x1.286]VykF7BpO3NFT550xU7Tx1w==[/tex]上的均匀分布, [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]服入指数分布[tex=1.786x1.357]NAcaUWG0M+fOpH6/Gh1yyQ==[/tex] .试求[tex=6.643x1.357]y80Y546TKJ9w+MUm0oMHBg==[/tex],[tex=6.286x1.357]k/hzUMjV7geOFY7iA5ZJqQ==[/tex]的概率密度.

答案：

解 因 [tex=4.571x1.357]rHJibQ4vhE3aD48pvLleHQ==[/tex], 即其概率密度及分布函数分别为[tex=10.643x2.429]OLdhkgwiN7f8y1keeGS2hqOTCCO0YRDLwxjE9jvmMYev0ueIVO+RJYOPR8mjbacIYRiqSC759E+V9EHtRZClAQ==[/tex],[tex=10.786x3.643]TEOndWpbV5/5mY+qUFvG97phMcazUKngsk2Y+RVrGkvezthWeOGQ2vJqlkjGTWYZW3aEcOjzBa60s/H80JjiRuet1BY2GQKxCOsuOSiJdPg=[/tex][tex=3.0x1.357]N9Q6sbzdsj5c2chUmRBl+w==[/tex], 即其概率密度及分布函数分别为[tex=11.071x3.357]2uDyFin9peAIJ4ssgmWVE+GfT9mMQoNpeMeSfiuJEkzpuc723zJJaRpotfWvfEKvrLYflq646SlPgE/j3o9zaF3RxwTX//HxzkzagUpo50b2rPv/+l1bmKBciS98hknA[/tex],[tex=12.0x3.357]+mfkalSO2Jdykp3KCmQVf3qGgrJSOuSDNbPHEsqTTMhntzNIOD0NJJKb5/XNi/YAnZWdhZCuCPUsTf3PLn3Zvu3vSI7mhMNtGn8yQ83U5717SYKEojWc3t0cFLXm3Yds[/tex](1) [tex=7.143x1.286]UwlCH+LivSrZK2EEwmTlwE/8mHfjkZvC2+v6liK96jg=[/tex]的分布函数为[tex=9.143x1.286]4LLiNHE4/CvsP6Pv+ikmTPO3OZPQYs1dkpQha5/WQJo=[/tex][tex=12.143x4.643]luxnYXPz0zFuH3jflAxrJv6y8py0Tx5M9eU1ia+69tqJB0i62UTTw7MFqOo/ZdHfhhcVbQe7Nha+isST6vjfO8tlEe7BANZIlm+FBo/6TRXPDJejib8B91vt/aZCJnC7olxgqqe6SZcV3Kfu2sMmin2CXAF4kM4MCBKGn3/tkPM=[/tex]故[tex=17.143x4.5]K4ts5/jdcRGvzVkL60D3ymJoXBxWXnAEP8rC5p7QrP24SbK87tuuS8NVc2814GM8YCPSqfzp4eSdvPZHlAyxFrZ16jerNxturO+nPSbYumu6aO9ohuHuliPbMwlel52bCPeRIXsX3qmNmPQRDzrRcGsznlRRR8brJirCSliBN3g=[/tex](2)[tex=6.786x1.286]jRGiqybHGfEW9+4GJpq9VQs6HN9Lwvp1bNVFDyZ+0lU=[/tex]的分布函数为[tex=13.714x1.357]CpzHYzzqHkpFPzSPHp0rkB72EHNaOdIubL2oV6k6T1yPUfZcbvM/a0JfslFFWjMNHjlOzxg5tshEFjfxH8F2wA==[/tex][tex=13.786x4.5]luxnYXPz0zFuH3jflAxrJh174eYeGOxozn6Fb3Prsceet4thqseg4XTA4crN+5tJ0FJkiQS9FTA/PNOa8l9AdKTmf+eCPLNv63XX82qmsiWLDnkIYUYSW+6cdH8XCgYFxG7uXGQV/ZaAYFkceiGRpg==[/tex]故[tex=16.643x2.429]VcemyaqwrEoxa+6vq06Xm9E8FgYrGJKFiNKhktpQOBwtoBNid6C5NpqIGKySHDF/WmNXzCWv99jc/4DanNclYXGrJ42V1L2I/kFO9VB1pJo=[/tex]

举一反三

内容

0
[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 服从参数 [tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex] 的指数分布,而 [tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex] 是服从 [tex=2.0x1.357]13hO1E7iMz89y/8d++Roag==[/tex]上的均匀分布的随机变量.求 [tex=4.429x1.357]s28QpA3Jw/YTu78REq5g0WAL1Ak3EpFCjxCSdrBCPPc=[/tex] .
1
设[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]与[tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex]相互独立且都服从 [tex=2.286x1.357]wnjWedGSaRozNOGeVeBjbA==[/tex]上的均勿分布，求随机变量[tex=3.714x1.143]bAuRnS0EozFwlT9vxryEWA==[/tex]的密度函数。
2
设[tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex]服从参数为 1 的指数分布,[tex=2.286x1.0]9/9iwGqXp5QMYqkNTltYDNEowzysbRa2vywE4TxIMeI=[/tex],求[tex=2.214x1.357]ocoZdV18P73QTNWKFIScyg==[/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
设二维随机变量 [tex=2.786x1.286]wsm6hZKLwoHLmpiSvjoPLA==[/tex]服从区域 [tex=15.429x1.286]bf7mxN/1XbjV+1U5hRGMJUL29bpbVhbED9m+nTCgXF2qosKQudDF0at83HHogwIkKA3E0KzQ3LgVTN7ZqY6wDA==[/tex] 上的均匀分布,求 [tex=0.857x1.0]N7iCrOsS+NNEUUlnsYCi1g==[/tex] 和 [tex=0.857x1.286]h9C4nePGcGllh55hxKIsUw==[/tex] 的边缘密度函数.