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单选题设总体,其中已知,是来自总体的样本,和分别是样本均值和样本方差,则下列结论中成立的是( )

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：2023-12-03 04:19:48

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设总体<img src="https://tihai-oss-cloud.itihey.com/img/cbced06aaef650f27acbe9b293ccddf6.png">,<img src="https://tihai-oss-cloud.itihey.com/img/f6ed1053a96dd91571ddb4121f6a52a2.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/c73568ae22111de34f970224f58d194f.png">的样本,<img src="https://tihai-oss-cloud.itihey.com/img/cbf871d770af81fb58929df9e23bb52a.png">为一组样本观测值,则参数<img src="https://tihai-oss-cloud.itihey.com/img/083fc5415026974dc76c3d4d243e95e0.png">的最大似然估计量为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/407d20c72f68ac2d608a8653c3ce16dd.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/92f1175123e8253e26f39cd099c24e93.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/093aa638a83f8e2b8e02dd92d8fea9ae.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/4e21bf22de9aade3b452dd4d90360954.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/2b86296892c09a4a4b6543f921fd5908.png">为正态总体<img src="https://tihai-oss-cloud.itihey.com/img/57ee6791543c8c66c636320eea526f42.png">的一组样本观测值,估计标准差为<img src="https://tihai-oss-cloud.itihey.com/img/5ff5b7923441ee73147f05a8f79fbd43.png">,要使对<img src="https://tihai-oss-cloud.itihey.com/img/69045b594fdc566ddce88c9ce7b40070.png">做出的估计与<img src="https://tihai-oss-cloud.itihey.com/img/69045b594fdc566ddce88c9ce7b40070.png">的真值的差距最多不超过<img src="https://tihai-oss-cloud.itihey.com/img/8d2fa4e46775c65d0a381f8016333130.png">的置信度为<img src="https://tihai-oss-cloud.itihey.com/img/eec9085496d8074e94e363b07efc3f17.png">,则样本容量<img src="https://tihai-oss-cloud.itihey.com/img/1dac517aff62a020fcb3bbd85e78ab3f.png">至少取( ).注:<img src="https://tihai-oss-cloud.itihey.com/img/b7bb1ebb6ca78d0003bf4d8d64d57e89.png">,<img src="https://tihai-oss-cloud.itihey.com/img/6f2935f24e8c1d8c1c27f168769f3aff.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/03dd862df51d246c9aac6326a1b9a199.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/09152aa0e6f7a574ea49d225c9fc7f65.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/109f50c14c35110e411048c35c08aab7.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/98fbcbd5fd8d7e091dea718deecb1ea0.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/161fcd5a12e8a3d5e2d2c4b89a3f59f7.png">为正态总体<img src="https://tihai-oss-cloud.itihey.com/img/57ee6791543c8c66c636320eea526f42.png">的一组样本观测值,计算得<img src="https://tihai-oss-cloud.itihey.com/img/95029cb544011f80d7758ec4185d66b4.png">,<img src="https://tihai-oss-cloud.itihey.com/img/da42749cc03fa7790f7fb9c9d3d0026e.png">,则<img src="https://tihai-oss-cloud.itihey.com/img/dcc7d44738f03504d7825f2ec182cdce.png">的一个置信度为<img src="https://tihai-oss-cloud.itihey.com/img/05e012039e532860b78a1c9e43424a78.png">的置信区间为( ).注:<img src="https://tihai-oss-cloud.itihey.com/img/d725a22676c16089e37e7af7e5f4b977.png">,<img src="https://tihai-oss-cloud.itihey.com/img/803484e3d17b90327c360aca66956b66.png">,<img src="https://tihai-oss-cloud.itihey.com/img/f26742312ea20e20f679329d6400e07e.png">,<img src="https://tihai-oss-cloud.itihey.com/img/378044723184ac25430a233b2aaace80.png">

A. <img src="https://tihai-oss-cloud.itihey.com/img/9913967476f85a7fc3ceb7f05d013ed9.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/d1a94c5612ec65209cafe556e15c3db2.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/098d1eb84fba566e73d2fc0ad264ed32.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/60d8bd98a6998c3abedfc43ea3abe318.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/b4091ce8ff5fea738b1992fd920d0270.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/c73568ae22111de34f970224f58d194f.png">的样本,且<img src="https://tihai-oss-cloud.itihey.com/img/03a42a62eec9130b7fa8731bf1d00085.png">,<img src="https://tihai-oss-cloud.itihey.com/img/cca5a0c2c0759e372389dfaadb71ad9b.png">,<img src="https://tihai-oss-cloud.itihey.com/img/81f13e41e7cc90d511fc1f215604a5ff.png">均为总体均值的无偏估计量,则<img src="https://tihai-oss-cloud.itihey.com/img/c275b49ab90b633fe382ccf02ff3e1bd.png">的大小关系为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/3e520fb5024e20cd6ed554f72a54915b.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/be508cf1d3dddbba04aff0c84e585498.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/b47517d5f1c5af8002eaab8b8ccba77a.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/591999fb65a4bc93e91248cc4edeabd6.png">

已知<img src="https://tihai-oss-cloud.itihey.com/img/95aa6064f00cc276ff2f4479a0532623.png">,<img src="https://tihai-oss-cloud.itihey.com/img/29151cccba70c4479fb2f87d6871c0fa.png">,设<img src="https://tihai-oss-cloud.itihey.com/img/051d4441d078ce6aa56cbed49fb79f65.png">为来自正态总体<img src="https://tihai-oss-cloud.itihey.com/img/2f5ceb3264a24dbb46809856a5e4e4fc.png">的样本,<img src="https://tihai-oss-cloud.itihey.com/img/9c49620513cba6101f95743347b345c1.png">,那么, <img src="https://tihai-oss-cloud.itihey.com/img/8a67762bec84b3b3b4ceba49a6a993f2.png">( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/e7342bd2434ea083108a9337995cf5c8.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/c194588d15c4caef7a0ad2a8e243b898.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/2ef407ee98678d9d8fdea53a8a4012f1.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/d77cfe2d9e61523ff19fe067fbc0d5d3.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/038c70ae945ecb904db37483e150e54d.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/c73568ae22111de34f970224f58d194f.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://tihai-oss-cloud.itihey.com/img/5bbf7375b52558e012e1e3887c3ebb1e.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/2de661ff4db4ef14931d9c55e7613547.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/4791ae21bb39b4b54f9553659dd7b9ae.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/0b2078af1e618980acb4d0dfbffc8dce.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/cbced06aaef650f27acbe9b293ccddf6.png">,<img src="https://tihai-oss-cloud.itihey.com/img/f6ed1053a96dd91571ddb4121f6a52a2.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/c73568ae22111de34f970224f58d194f.png">的样本,<img src="https://tihai-oss-cloud.itihey.com/img/1a7db69864b4731f67f0fbdcff93cb41.png">为一组样本观测值,则参数<img src="https://tihai-oss-cloud.itihey.com/img/083fc5415026974dc76c3d4d243e95e0.png">的矩估计值为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/407d20c72f68ac2d608a8653c3ce16dd.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/093aa638a83f8e2b8e02dd92d8fea9ae.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/7a057470acdf6e0fb6603b786cd7fa4c.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/883710f46ed22cd758005593a8ac9e36.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/a8d5ef5b8b397676ba6ca5df9995f34b.png">,其中<img src="https://tihai-oss-cloud.itihey.com/img/1ddcea360a9d0483e66a3fce43729c9d.png">已知,<img src="https://tihai-oss-cloud.itihey.com/img/f734a78e6dd474df9112e91898f803e8.png">是来自总体<img src="https://tihai-oss-cloud.itihey.com/img/c73568ae22111de34f970224f58d194f.png">的样本,<img src="https://tihai-oss-cloud.itihey.com/img/0dd079b4efc7fd93aebce16cfa9dd430.png">和<img src="https://tihai-oss-cloud.itihey.com/img/0969eee43c46ea796b363849769d6fa0.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://tihai-oss-cloud.itihey.com/img/b2f955153b55537fc09a3604ee9b2256.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/923f25b9969409757cf6325c7debbd20.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/62933090454010d0394c9045e87dd98a.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/9f08de0d7a026168537c568d9c5be565.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://tihai-oss-cloud.itihey.com/img/47ee07d4134694aa351b917f331a9dcb.png">. 假设每包糖果的实际质量服从正态分布<img src="https://tihai-oss-cloud.itihey.com/img/57ee6791543c8c66c636320eea526f42.png">. 要检验每包糖果的平均质量(即总体期望<img src="https://tihai-oss-cloud.itihey.com/img/2139c21a5768bcefe28e92abb5fc3a77.png">)与规定质量是否相符,应提出的原假设<img src="https://tihai-oss-cloud.itihey.com/img/760fb8befb04bf6fef1836514fa5144e.png">为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/d704e891296f582780dc0b761978afc3.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/55d99a4a24579b830daa59980ad5c2e8.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/02d761de2471fe227a6fc9289c13991f.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/9d53051a46444032a0d13f10dff8b2ad.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/ec0216ec175bba486c307009862f5d6f.png">,<img src="https://tihai-oss-cloud.itihey.com/img/f734a78e6dd474df9112e91898f803e8.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/c73568ae22111de34f970224f58d194f.png">的样本,则该样本的密度函数为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/b23f5c4437f317176fe691c814b4f6e1.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/03429683db9e459ba2e83024ab5c8694.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/dbed00b32c9ef204e7df0f6da101614f.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/dc505a5b5ce6f5a923c1da33def6f900.png">

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