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单选题设为来自总体的样本,且,,均为总体均值的无偏估计量,则的大小关系为( )

A.

B.

C.

D.

概率论与数理统计A课程封面

学科：概率论与数理统计A

时间：2024-01-06 11:16:33

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设总体<img src="https://p.ananas.chaoxing.com/star3/origin/33593d2ec3a14f1a071b3c309aa11260.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/a128b229db9604ef7b76c27ad9fe8bc1.png">为来自总体<img src="https://p.ananas.chaoxing.com/star3/origin/bbc2581b1b4ee1fc2aca8a685c3048f3.png">的样本,<img src="https://p.ananas.chaoxing.com/star3/origin/541e81328da360a91c5dfe4e8bea4fcd.png">为一组样本观测值,则参数<img src="https://p.ananas.chaoxing.com/star3/origin/9c0a76305174369fd8c948052a271634.png">的最大似然估计量为( )

A. <img src="https://p.ananas.chaoxing.com/star3/origin/9aee8b26f346c3e8b24cf15d38d784ac.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/f7366c6d71d439108229ff8a0868d4ab.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/1ec1bd790dd32433d265a46471ed37c1.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/73e7a6701d6580e7098640933fdb96b1.png">

设<img src="https://p.ananas.chaoxing.com/star3/origin/3a927a92e62be7b599f407aa418454a2.png">为正态总体<img src="https://p.ananas.chaoxing.com/star3/origin/d99cb7ea26668817c280ae55675017e6.png">的一组样本观测值,估计标准差为<img src="https://p.ananas.chaoxing.com/star3/origin/64a2cdc2c72b48dbfcf7bca71d393110.png">,要使对<img src="https://p.ananas.chaoxing.com/star3/origin/cc1373ca1e2fd4642da85f81af0ae976.png">做出的估计与<img src="https://p.ananas.chaoxing.com/star3/origin/cc1373ca1e2fd4642da85f81af0ae976.png">的真值的差距最多不超过<img src="https://p.ananas.chaoxing.com/star3/origin/4f092ed8f56e881590d997aa242db59a.png">的置信度为<img src="https://p.ananas.chaoxing.com/star3/origin/8a34e3796f55af46cb327a2ec13349c5.png">,则样本容量<img src="https://p.ananas.chaoxing.com/star3/origin/570f18e4498ea5e008d7bbd8.png">至少取( ).注:<img src="https://p.ananas.chaoxing.com/star3/origin/45c6cd863a45df2d45988a28e4b0e2c9.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/a3fe195c06d9ff6066bdd9efa2fb1e66.png">

A. <img src="https://p.ananas.chaoxing.com/star3/origin/655388cd97fa74423eaed4666cf6eb91.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/c8ebaae7786b3cfad1956919ca278832.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/cc262463495c822cb8a65fd19e4135d1.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/5b3b5beb43aed638db1d714decac83b3.png">

设<img src="https://p.ananas.chaoxing.com/star3/origin/50103ceea2bb1bfa47774c1025ef6cb6.png">为正态总体<img src="https://p.ananas.chaoxing.com/star3/origin/d99cb7ea26668817c280ae55675017e6.png">的一组样本观测值,计算得<img src="https://p.ananas.chaoxing.com/star3/origin/eff6e5ac36336db4afd2b70fc2727143.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/de667885345fd44d2114e6e584c2d480.png">,则<img src="https://p.ananas.chaoxing.com/star3/origin/e3513e808fc435826b1d8c9a1ac0d677.png">的一个置信度为<img src="https://p.ananas.chaoxing.com/star3/origin/73cd213d349021e8e7245b826729daef.png">的置信区间为( ).注:<img src="https://p.ananas.chaoxing.com/star3/origin/3441f3b0dac21d227872a5501ad2d21d.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/c4b5e0cf8be82eeacb4a6ad7539d3c94.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/e8f43478c29cb69fb0cc034a0fd2b794.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/e000bbda79dc42e783e7e887b84f97dc.png">

A. <img src="https://p.ananas.chaoxing.com/star3/origin/c45a66fc9151816c261b97a25c737b7e.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/84736f8690669c425dbd6260228a2d05.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/02e94182fe9d7bbd0a2dd26ad2c93b7f.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/e220da55c4206985600ae1c228498e3e.png">

设<img src="https://p.ananas.chaoxing.com/star3/origin/c13b13545c6ccf897b8b6d58d4a75e93.png">为来自总体<img src="https://p.ananas.chaoxing.com/star3/origin/bbc2581b1b4ee1fc2aca8a685c3048f3.png">的样本,且<img src="https://p.ananas.chaoxing.com/star3/origin/7b4c2fc72d4412403d2b47776725d6cf.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/7614a0441010d014850af89b6f6875c1.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/de3abd23777718195b4383a773bdb634.png">均为总体均值的无偏估计量,则<img src="https://p.ananas.chaoxing.com/star3/origin/5cce5b6502b41de45b6a17b87910e336.png">的大小关系为( )

A. <img src="https://p.ananas.chaoxing.com/star3/origin/0060831246a341eb1a1e0022032e9db2.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/a5e89cc790c10bf2f53c670483f736f6.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/ce772b9bc0fd2f99c96756b99e9d987c.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/93b70c8638430c692b441894926fecf6.png">

已知<img src="https://p.ananas.chaoxing.com/star3/origin/b0e44883c9be2cdf7357632fe0a84210.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/92d4387e2782be10772a2987b18c2b3e.png">,设<img src="https://p.ananas.chaoxing.com/star3/origin/4d29e1a041a6e4567ad810fda5eee67b.png">为来自正态总体<img src="https://p.ananas.chaoxing.com/star3/origin/c3439330d7af4f847917f962d4b1d813.png">的样本,<img src="https://p.ananas.chaoxing.com/star3/origin/cb5229b9dfa0de458e634f14ee5e844e.png">,那么, <img src="https://p.ananas.chaoxing.com/star3/origin/9ac20ba1a54c062278a4c0602f36ab4c.png">( )

A. <img src="https://p.ananas.chaoxing.com/star3/origin/4ecf7c3a9e438c8fd65bd8d42145f7fa.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/ae6998d47dd69dd46249dc076ea321a9.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/6fb23c0a0dd0e2cc56025e977392d425.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/93a1db3bcb1e95603c625cefc6acbc22.png">

设<img src="https://p.ananas.chaoxing.com/star3/origin/ae1c98b4def8a5e3913a14b29b9d87a7.png">为来自总体<img src="https://p.ananas.chaoxing.com/star3/origin/bbc2581b1b4ee1fc2aca8a685c3048f3.png">的样本,那么下面总体均值的估计量中,( )是有偏估计量

A. <img src="https://p.ananas.chaoxing.com/star3/origin/d78ef8c90b98c00cd40de013322b80ff.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/49f3cce5293471ca4c8f6803625b6676.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/00d01a566cbe73c213918a20c39a3086.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/63653f7509c25734fadb0b7d2328f207.png">

设总体<img src="https://p.ananas.chaoxing.com/star3/origin/33593d2ec3a14f1a071b3c309aa11260.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/a128b229db9604ef7b76c27ad9fe8bc1.png">为来自总体<img src="https://p.ananas.chaoxing.com/star3/origin/bbc2581b1b4ee1fc2aca8a685c3048f3.png">的样本,<img src="https://p.ananas.chaoxing.com/star3/origin/2b244f3297679904633a3e32fbfe50a7.png">为一组样本观测值,则参数<img src="https://p.ananas.chaoxing.com/star3/origin/9c0a76305174369fd8c948052a271634.png">的矩估计值为( )

A. <img src="https://p.ananas.chaoxing.com/star3/origin/9aee8b26f346c3e8b24cf15d38d784ac.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/1ec1bd790dd32433d265a46471ed37c1.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/a613e7443070fde86a49264b9cb47ce3.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/0a0048f61b18d1471e43e47beaa7b3ef.png">

设总体<img src="https://p.ananas.chaoxing.com/star3/origin/f6f5045d1e140876c8cda157714e0581.png">,其中<img src="https://p.ananas.chaoxing.com/star3/origin/6a0e5ce76cab4d0dc433abb61f9c21b2.png">已知,<img src="https://p.ananas.chaoxing.com/star3/origin/3fe59ff7fe8951cf75c4406c6801063a.png">是来自总体<img src="https://p.ananas.chaoxing.com/star3/origin/bbc2581b1b4ee1fc2aca8a685c3048f3.png">的样本,<img src="https://p.ananas.chaoxing.com/star3/origin/b4aede70fe06675668d917754ac392da.png">和<img src="https://p.ananas.chaoxing.com/star3/origin/81d2a532c6091dbbd77eb97bc1ee6c72.png">分别是样本均值和样本方差,则下列结论中成立的是( )

A. <img src="https://p.ananas.chaoxing.com/star3/origin/016260fbf6093986be06a25b01f72960.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/d177b8c9f82e7ff81fe4b0b38d1b194d.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/b0fc98881fb101479b6e6478dc2c580c.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/9a09347f34a85c98d78b73f4ee625245.png">

某糖果厂用自动包装机包装糖果,规定每包质量为<img src="https://p.ananas.chaoxing.com/star3/origin/4ec859ccc6aa7135086e3338733dd356.png">. 假设每包糖果的实际质量服从正态分布<img src="https://p.ananas.chaoxing.com/star3/origin/d99cb7ea26668817c280ae55675017e6.png">. 要检验每包糖果的平均质量(即总体期望<img src="https://p.ananas.chaoxing.com/star3/origin/748a4d640b7eec17a7b791c82a2b0824.png">)与规定质量是否相符,应提出的原假设<img src="https://p.ananas.chaoxing.com/star3/origin/a62c595412f4cd94d7402f8be50c9a75.png">为( )

A. <img src="https://p.ananas.chaoxing.com/star3/origin/e8564d0b04286c720d5abdb9d17e0f7a.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/c20a5baac7688bd8326cb7d29a10b46a.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/ce485037dbb5de43979aa641ffb6b7f0.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/80e9eb97bb3cc28a7e54919bf4e3bcd0.png">

设总体<img src="https://p.ananas.chaoxing.com/star3/origin/e48fbf96f341e582506e06112f824aad.png">,<img src="https://p.ananas.chaoxing.com/star3/origin/3fe59ff7fe8951cf75c4406c6801063a.png">为来自总体<img src="https://p.ananas.chaoxing.com/star3/origin/bbc2581b1b4ee1fc2aca8a685c3048f3.png">的样本,则该样本的密度函数为( )

A. <img src="https://p.ananas.chaoxing.com/star3/origin/907dca899d841f2561d5c14b0181a572.png">B. <img src="https://p.ananas.chaoxing.com/star3/origin/2e5e6d2a3d34e8ceaae9538db39392fe.png">C. <img src="https://p.ananas.chaoxing.com/star3/origin/10d87d2c6bf6f806c0e8fb869b804ade.png">D. <img src="https://p.ananas.chaoxing.com/star3/origin/3891a1151b0d5e31e3088d1eb68cce24.png">

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