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单选题设,为的一个样本,分别表示参数的矩估计和极大似然估计,则

A.

B.

C.

D.

概率论与数理统计-2025春季课程封面

学科：概率论与数理统计-2025春季

时间：2025-04-23 08:41:54

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设总体<img src="https://tihai-oss-cloud.itihey.com/img/bd7ee51d0fa578e105aa9960a2eac85e.png">的密度函数为<img src="https://tihai-oss-cloud.itihey.com/img/761b888d1d464f6be420c5bee0f90f61.png">,其中<img src="https://tihai-oss-cloud.itihey.com/img/3a9c7034e2f0109011c96ce828086d1a.png">,<img src="https://tihai-oss-cloud.itihey.com/img/7659b1a1079005a67c8b3c50653b01c8.png">=

A. <img src="https://tihai-oss-cloud.itihey.com/img/3a257d18d5a246d11e61fe9b69e75e2a.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/25dc02fa4dd67b6cef20dadf578ccb18.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/fc1ba2942cd50870055fcc4ecb585b90.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/bdbe22a9df8258c3c53df6fb713a584f.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的数学期望为<img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">,<img src="https://tihai-oss-cloud.itihey.com/img/48b851da5bf8b6ea2b45a5438a7ae0a0.png">是来自总体<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的简单随机样本,则下列命题中正确的是

A. <img src="https://tihai-oss-cloud.itihey.com/img/27d4b22f79357679a6771d6863396228.png"> 是 <img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的无偏估计B. <img src="https://tihai-oss-cloud.itihey.com/img/e7f79d75a2697ea5c8d535f888c91b0a.png"> 是 <img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的最大似然估计C. <img src="https://tihai-oss-cloud.itihey.com/img/e7f79d75a2697ea5c8d535f888c91b0a.png"> 是 <img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的相合估计D. <img src="https://tihai-oss-cloud.itihey.com/img/e7f79d75a2697ea5c8d535f888c91b0a.png"> 不是 <img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的估计量

设<img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">是总体<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的一个参数,<img src="https://tihai-oss-cloud.itihey.com/img/d836560b9296a457541b7a140b1e648e.png">是<img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">的一个估计量,且<img src="https://tihai-oss-cloud.itihey.com/img/11768729308b4c5eaad73b32fb1d2c59.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/d836560b9296a457541b7a140b1e648e.png">是<img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">的

A. 一致估计B. 有效估计C. 无偏估计D. 一致和无偏估计

设<img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">是总体<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的参数,<img src="https://tihai-oss-cloud.itihey.com/img/31c57355ee10a09541fe9cdc31659c09.png">为<img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">的置信度为<img src="https://tihai-oss-cloud.itihey.com/img/3d8a0f2f4b5d9fbbe7c8603eb814da87.png">的置信区间,即<img src="https://tihai-oss-cloud.itihey.com/img/c17184a08ac4db451de7f2eebeb77b10.png">,这就是说

A. <img src="https://tihai-oss-cloud.itihey.com/img/31c57355ee10a09541fe9cdc31659c09.png">以概率 <img src="https://tihai-oss-cloud.itihey.com/img/2b99a4ea72301a7b368d800fa07aa1c6.png">包含 <img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">以 <img src="https://tihai-oss-cloud.itihey.com/img/2b99a4ea72301a7b368d800fa07aa1c6.png">的概率落入 <img src="https://tihai-oss-cloud.itihey.com/img/31c57355ee10a09541fe9cdc31659c09.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">以 <img src="https://tihai-oss-cloud.itihey.com/img/d799c28a9cac0ffa29afd9ef4a48f1fa.png">的概率落在 <img src="https://tihai-oss-cloud.itihey.com/img/31c57355ee10a09541fe9cdc31659c09.png">之外D. <img src="https://tihai-oss-cloud.itihey.com/img/31c57355ee10a09541fe9cdc31659c09.png">以概率 <img src="https://tihai-oss-cloud.itihey.com/img/d799c28a9cac0ffa29afd9ef4a48f1fa.png">包含 <img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">

<img src="https://tihai-oss-cloud.itihey.com/img/6c5c537e9c7e6d5bab0f870fb6649694.png">为<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的样本,<img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的置信度为<img src="https://tihai-oss-cloud.itihey.com/img/2b99a4ea72301a7b368d800fa07aa1c6.png">的置信区间的长度随<img src="https://tihai-oss-cloud.itihey.com/img/660e847f6399a552faa2424a0d1e5343.png">的增大而

A. 增大B. 减小C. 不变D. 有时增大,有时减小

设<img src="https://tihai-oss-cloud.itihey.com/img/7f9ee70ef65a8103c490edb2972467c9.png">,<img src="https://tihai-oss-cloud.itihey.com/img/ae2d36b160f092244a9fa49499e96e72.png">为<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的一个样本,<img src="https://tihai-oss-cloud.itihey.com/img/f78534e11c2fa473d2883a3955bfcc5d.png">分别表示参数<img src="https://tihai-oss-cloud.itihey.com/img/1ee47c09bdcbf14e9e8a419d2a3a8b8b.png">的矩估计和极大似然估计,则

A. <img src="https://tihai-oss-cloud.itihey.com/img/61c038ca5470d595290a975704a92bd0.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/13eedcba3dc32e2c7c6dad093c385f5a.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/75ec489f3643f8e7a195f5d3e858a117.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/3f57660d4c497684bf08f971ea44df4d.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/4d3e71ef142da2a93881311c8c936498.png">,<img src="https://tihai-oss-cloud.itihey.com/img/21a803c5ccebe7d0c9f1a6361e66602d.png">为<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的样本,则<img src="https://tihai-oss-cloud.itihey.com/img/b09362cb24e2f539c6e73151a125533e.png">和<img src="https://tihai-oss-cloud.itihey.com/img/31a4842d03c30bc4baf79e1f8121c1bf.png">的极大似然估计为

A. <img src="https://tihai-oss-cloud.itihey.com/img/cea31212c3ad15af0defd8e0084ad08b.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/f84a903b8ca3de1b68af955b1d3011c5.png">,<img src="https://tihai-oss-cloud.itihey.com/img/6228f4a3c0411280764c78d7a6c2bf51.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/eecf75f81796c775925e6d9c4543aea0.png"> ,<img src="https://tihai-oss-cloud.itihey.com/img/f84a903b8ca3de1b68af955b1d3011c5.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/699311579c64737a93dc76c702beea1a.png">,<img src="https://tihai-oss-cloud.itihey.com/img/699311579c64737a93dc76c702beea1a.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/be896aef9cf166c0e53054f72f643563.png">均未知,则<img src="https://tihai-oss-cloud.itihey.com/img/6ba04bd1c15f602968314f1ec85dddb7.png">是

A. <img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的无偏估计B. <img src="https://tihai-oss-cloud.itihey.com/img/fba25168ed55447492cf580b6e582a4a.png">的无偏估计C. <img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的矩估计D. <img src="https://tihai-oss-cloud.itihey.com/img/fba25168ed55447492cf580b6e582a4a.png">的极大似然估计

<img src="https://tihai-oss-cloud.itihey.com/img/01cfa7114e881c14e3f846dbb167dc79.png">是总体<img src="https://tihai-oss-cloud.itihey.com/img/bea1e30975a1c8c3499a86d7e5a41422.png">的样本,且<img src="https://tihai-oss-cloud.itihey.com/img/129eb7f19db5af19541037115fbe0eb6.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的无偏估计是

A. <img src="https://tihai-oss-cloud.itihey.com/img/d71cdacc29e174336132337007ff3f3f.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/810ec19f8b14f952af7ff7350157807e.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/bd29db39f465e3bfb91fbe5f26cc545f.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/8aa023e696ee8b75865ee3abe4b5e64b.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/0c583d7e11db4cab13302ef22acc7cea.png">是来自<img src="https://tihai-oss-cloud.itihey.com/img/558ebe44112d9f67458e6874620b2da6.png">的样本,则【】是总体均值<img src="https://tihai-oss-cloud.itihey.com/img/cd1373314da89a501d9373c9f491b537.png">的无偏估计

A. <img src="https://tihai-oss-cloud.itihey.com/img/7e4d36255e3889cf87233b2a07734b6c.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/1d2d9cd25fe41ee2ae906ed06bd43071.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/fd8084dc48de0a98e874a689531efa49.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/5a438c25dc8859010e0086e3ac16922a.png">

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