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单选题设随机变量X的概率密度函数为f(x)=,则其分布函数F(20)的值为( )

A.

B.

C.

D.

概率论与数理统计课程封面

学科：概率论与数理统计

时间：2025-12-25 00:58:52

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设随机变量X的概率密度为f(x)=<img src="https://tihai-oss-cloud.itihey.com/img/8787d116e44d352ac2e32df603ffb651.png">,则k等于( )

A. 1B. <img src="https://tihai-oss-cloud.itihey.com/img/d81dde6b8b79560cf6110cbdda8eb45d.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/db49eec64a8074e720cde8c1866a92ba.png">D. 0

设随机变量X的概率密度为f(x)=<img src="https://tihai-oss-cloud.itihey.com/img/cdc83e411fd3455200df919a580d7262.png">,则P{-2<X<<img src="https://tihai-oss-cloud.itihey.com/img/d81dde6b8b79560cf6110cbdda8eb45d.png">}=_______

A. <img src="https://tihai-oss-cloud.itihey.com/img/29e62267addb729508765e5e78adb73d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/e14dcba6644f7d6ae0246ab6cf0a94d6.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/6489ec0e8343e902b1622cf065452e89.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/71c1498523cb361a960b6566d47066e3.png">

设随机变量X的概率密度函数为f(x)=<img src="https://tihai-oss-cloud.itihey.com/img/3de1d610c184bbbe96558b56e15146c3.png">,则其分布函数F(20)的值为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/d81dde6b8b79560cf6110cbdda8eb45d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/03e62125dff3fa9a165935ace94ddf1e.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/db49eec64a8074e720cde8c1866a92ba.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/24a66969b07d5ae7dd57285ac5db702b.png">

设某随机变量的概率密度函数为f(x)=<img src="https://tihai-oss-cloud.itihey.com/img/ff0952a7cbe7c1c46977db2884a02458.png">,则常数c的值为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/286b0b63a367bb7f26530cc34b549984.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/d81dde6b8b79560cf6110cbdda8eb45d.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/e456af92841b3db4789575527eca6357.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/03e62125dff3fa9a165935ace94ddf1e.png">

下列关于连续性随机变量的叙述正确的是______. (1)都具有有限或无限可数(列)的值; (2)分布函数都是右连续,但不是左连续; (3)分布函数都没有跳跃; (4)分布函数都是左右连续的; (5)都具有无限多的值

A. 仅限(1)和(3)B. 仅限(3)和(5)C. 仅限(3)(4)和(5)D. 仅限(1)(3)和(4)

设连续型随机变量X的分布函数为F(x)=<img src="https://tihai-oss-cloud.itihey.com/img/b2f1ac58425813831304f05bd0a015ea.png">,则P{X=<img src="https://tihai-oss-cloud.itihey.com/img/00383843845cea7e14e13382918ca71d.png">}=_____

A. <img src="https://tihai-oss-cloud.itihey.com/img/fe6e267b1e70bcf9f5f9c6ed2431af61.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/d0e195d02601ffa7762316e2294d8139.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/774dd4431d40538ecc2beac4d7baccd1.png">D. 0

设<img src="https://tihai-oss-cloud.itihey.com/img/8e0fdd2bb5b7f0e3fd3c6ec96cd4be28.webp">为两个分布函数,其相应的概率密度<img src="https://tihai-oss-cloud.itihey.com/img/3a08262f822ce1b30afdd50777735d91.png">是连续函数,则必为概率密度的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/3b0244a1ed6fa662d4b6bc1046b059e5.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/45265a2e3d6206ca584c504938f20276.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/d5a25c655fe0c442969a28c6f79c5319.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/ef2b0373c7132f349cacce6b91184e43.png">

设连续型随机变量X的密度函数为f(x),分布函数为F(x),x是任意实数,则下列选项正确的有( )

A. P(X = x)= F(x)B. P(X = x)= f(x)C. <img src="https://tihai-oss-cloud.itihey.com/img/174f62d348d2628af537403201d4607b.webp">D. P(X = x)= 0

下面四个选项中,( )不是概率密度

A. <img src="https://tihai-oss-cloud.itihey.com/img/1affc7f0f3a73654e14352c31bbf5b64.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/fa155c3a10ab4ae4e39bde8a5ddf6a88.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/05e31fa3d920af591770b4e95de79a1e.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/252b7c795ee27984fff13608f4cec5d3.png">

连续型随机变量可以解释现象:概率为零的随机事件未必是不可能事件

A. 正确B. 错误

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