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单选题 设随机变量X,Y相互独立,且,则D(Z)=( )

A. 8

B. 16

C. 28

D. 44

概率论与数理统计课程封面

学科：概率论与数理统计

时间：2026-01-11 00:48:14

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题目1
单选题
设随机变量X,Y相互独立,且<img src="https://tihai-oss-cloud.itihey.com/img/776113130042004d202b5cca2e464532.png">,则D(Z)=( )
A. 8B. 16C. 28D. 44
题目2
单选题
设10个电子管的寿命<img src="https://tihai-oss-cloud.itihey.com/img/356aa3dbec44b69536d583c17a9f3686.png">独立同分布,且<img src="https://tihai-oss-cloud.itihey.com/img/964fc6027e3765600536ed7692fb23df.png">,则10个电子管的平均寿命Y的方差D(Y)=_______
A. 0.2AB. 0.1AC. 10AD. A
题目3
单选题
设随机变量<img src="https://tihai-oss-cloud.itihey.com/img/36c1fd32a4b316e7829cd3ce1ac3a9f8.png">,且相互独立,则D(X-Y)等于( )
A. -1B. 5C. 4D. 3
题目4
单选题
设随机变量X服从参数为&lambda;的指数分布,试求<img src="https://tihai-oss-cloud.itihey.com/img/f8c9d0b1c4ac354d288cb3382b3a46db.png">
A. <img src="https://tihai-oss-cloud.itihey.com/img/d89bf6efe133652ae209eb3bbfb397c6.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/e63ce294836549d8d93b5eaa1122a273.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/0c0c627f9ffe4374353cb8526c483a41.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/8e3fa1f33f1d04794540fc6e822a7ffc.png">
题目5
单选题
随机变量X的分布律如下表,则D(X)=( ). <img src="https://tihai-oss-cloud.itihey.com/img/4cc2a40ab9ebc901478c1e39e712476e.png">
A. <img src="https://tihai-oss-cloud.itihey.com/img/ff6de39e8282e26757ffa09bf0dfe0ec.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/e83aa94113c4fda66904e24fb61c60e1.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/3bc6129c6b5a287984617330b6e8a019.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/e469764605fbe65fad80c00a4aa28b9c.png">
题目6
单选题
设随机变量<img src="https://tihai-oss-cloud.itihey.com/img/c9a86bdc61ddc5f371bea783a1063e4e.png">,Y服从参数为3的泊松分布,且X与Y相互独立,则D(X+Y)=
A. 3B. 4C. 5D. 7
题目7
单选题
设随机变量X的概率密度为<img src="https://tihai-oss-cloud.itihey.com/img/6b2917dcb264b60d2e89df1bed9d1523.png">,则D(3X+2)=( )
A. 1B. <img src="https://tihai-oss-cloud.itihey.com/img/d0e195d02601ffa7762316e2294d8139.png">C. 4D. <img src="https://tihai-oss-cloud.itihey.com/img/806f9b59238976ae6cc47c9ee80b137e.png">
题目8
单选题
对任意随机变量X,若D(X)存在,则D[D(D(X))]等于( )
A. 0B. XC. D(X)D. <img src="https://tihai-oss-cloud.itihey.com/img/a9287fc36a60d802c9e2c42fcb311e71.png">
题目9
单选题
设随机变量X的方差存在, D(X)&gt;0,则以下结果正确的是
A. D(X)&gt;D(1-X)B. D(X)&lt;D(1-X)C. D(X)=D(1-X)D. D(X)+D(1-X)=1
题目10
判断题
随机变量的方差为描述变量取值偏离平均值的平均偏离程度
A. 正确B. 错误
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