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单选题设为来自总体的样本,且、,、是未知参数,取的以下无偏估计,其中( )最有效

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：2023-12-24 10:13:22

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下列描述不正确的是( )

A. 用样本方差估计总体方差B. 矩估计的思想是用样本矩的连续函数估计相应总体矩的连续函数C. 用样本均值估计总体均值D. 总体参数的矩估计量是唯一的

设总体X服从参数为λ的泊松分布,X1,X2,…,Xn是来自总体X的样本,<img src="https://tihai-oss-cloud.itihey.com/img/4f78a90b9c1cf5f198234b153426673a.png">,<img src="https://tihai-oss-cloud.itihey.com/img/aa508bf23cf1aeae53d1ec6fe6bd148f.png">,则下列结论不正确的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/d32c5fffa6070cf7e8d033d771ff368e.png">是λ的矩估计量,<img src="https://tihai-oss-cloud.itihey.com/img/0b54699644dc42fc7b312a0693e9533d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/042f635cffd2de2e356153d74984e33e.png">是λ的无偏估计量C. <img src="https://tihai-oss-cloud.itihey.com/img/d32c5fffa6070cf7e8d033d771ff368e.png">是λ的无偏估计量D. <img src="https://tihai-oss-cloud.itihey.com/img/042f635cffd2de2e356153d74984e33e.png">是λ的矩估计量,<img src="https://tihai-oss-cloud.itihey.com/img/667758f6169d32dd210aec0656492b66.png">

矩估计必然是( )

A. 有效估计B. 样本矩的函数C. 无偏估计D. 总体矩的函数

设总体<img src="https://tihai-oss-cloud.itihey.com/img/437299dcb57066aa948a140a21edab01.png">,其中<img src="https://tihai-oss-cloud.itihey.com/img/06531f6b3b07c46ccdc3191c54f6ee0e.png">为来自总体的样本,则下列统计量中不是未知参数<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的无偏估计的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/8ceb4ec04c768dfef675652a0c4e240d.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/2236d176b8a6998c0b4b38a3b929fb59.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/f02e054078e43020f694b872567ee69e.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/3c0ffe0c45486999dae1f09a191dd8dc.png">

设总体<img src="https://tihai-oss-cloud.itihey.com/img/a2dc3c81d3d5cffe3c09077f1188e3d7.png">,<img src="https://tihai-oss-cloud.itihey.com/img/1afd950894fce4fe04bcb3d3b9f86ede.png">为来自总体的样本,则总体参数<img src="https://tihai-oss-cloud.itihey.com/img/142ef139a8c5575b3688ddbd70049d88.png">的矩估计量为( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/390f9c6edd74b32e288a47dc215832f4.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/7155f1ce852858cf1b3003bab81e814d.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/828f6963feedbedabccdbcb3112a237e.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/516a67c6652900dcdef908c5989b64a1.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/3749723fbe8a1474c9d5085e06c833e2.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/e22a13f7edcffe98b7a922d3fe5be3b8.png">的样本,且<img src="https://tihai-oss-cloud.itihey.com/img/27344b8e07cd0ec70cf8c3ddf911aefa.png">、<img src="https://tihai-oss-cloud.itihey.com/img/c0fb24aea867ce70298a70474708d376.png">,<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">、<img src="https://tihai-oss-cloud.itihey.com/img/2107390c4d3868215a99042d7cbc888a.png">是未知参数,取<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的以下无偏估计<img src="https://tihai-oss-cloud.itihey.com/img/ddea6d9955ebebc1807afe55f4bf9d41.png">,其中( )最有效

A. <img src="https://tihai-oss-cloud.itihey.com/img/63bb8e5949e936b3586d218a9fa596c0.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/d0edd8cbef7c46c0d5da5297ad732e20.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/cc03cead35158f34e3d37470d37bdb30.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/e1b84f7a029f3b0b866d471529fdae75.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/3749723fbe8a1474c9d5085e06c833e2.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/e22a13f7edcffe98b7a922d3fe5be3b8.png">的样本,且<img src="https://tihai-oss-cloud.itihey.com/img/27344b8e07cd0ec70cf8c3ddf911aefa.png">、<img src="https://tihai-oss-cloud.itihey.com/img/c0fb24aea867ce70298a70474708d376.png">,<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">、<img src="https://tihai-oss-cloud.itihey.com/img/2107390c4d3868215a99042d7cbc888a.png">是未知参数,<img src="https://tihai-oss-cloud.itihey.com/img/f32c192991ce385511e1b065031cfcb3.png">,<img src="https://tihai-oss-cloud.itihey.com/img/7621db6c4b756ddada9c82b2499bc067.png">,下面结论错误的是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/945c3ec9d73cdbf4c20a42dbd1213885.png">比<img src="https://tihai-oss-cloud.itihey.com/img/427493f2490e48e014b692937d726cae.png">有效B. <img src="https://tihai-oss-cloud.itihey.com/img/f32c192991ce385511e1b065031cfcb3.png">是<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的无偏估计C. <img src="https://tihai-oss-cloud.itihey.com/img/427493f2490e48e014b692937d726cae.png">比<img src="https://tihai-oss-cloud.itihey.com/img/945c3ec9d73cdbf4c20a42dbd1213885.png">有效D. <img src="https://tihai-oss-cloud.itihey.com/img/7621db6c4b756ddada9c82b2499bc067.png">是<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的无偏估计

设总体<img src="https://tihai-oss-cloud.itihey.com/img/437299dcb57066aa948a140a21edab01.png">,<img src="https://tihai-oss-cloud.itihey.com/img/1afd950894fce4fe04bcb3d3b9f86ede.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/e22a13f7edcffe98b7a922d3fe5be3b8.png">的样本,若<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">、<img src="https://tihai-oss-cloud.itihey.com/img/2107390c4d3868215a99042d7cbc888a.png">均未知,则<img src="https://tihai-oss-cloud.itihey.com/img/335a22d904050e2f1f78f467845d3d92.png">是( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的矩估计量B. <img src="https://tihai-oss-cloud.itihey.com/img/2107390c4d3868215a99042d7cbc888a.png">的无偏估计量C. <img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的无偏估计量D. <img src="https://tihai-oss-cloud.itihey.com/img/2107390c4d3868215a99042d7cbc888a.png">的矩估计量

设<img src="https://tihai-oss-cloud.itihey.com/img/1afd950894fce4fe04bcb3d3b9f86ede.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/e22a13f7edcffe98b7a922d3fe5be3b8.png">的样本,且<img src="https://tihai-oss-cloud.itihey.com/img/27344b8e07cd0ec70cf8c3ddf911aefa.png">、<img src="https://tihai-oss-cloud.itihey.com/img/c0fb24aea867ce70298a70474708d376.png">均未知,则( )是<img src="https://tihai-oss-cloud.itihey.com/img/ed1f4d3c386f168f6dd71edf78235307.png">的无偏估计

A. <img src="https://tihai-oss-cloud.itihey.com/img/92e14ea577b7634b9b1dfd06a4eed99f.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/803637ec8e828b35741e2ca3d511d58a.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/b0b07dd3e4761ebd9ae504c9afdf720a.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/d9623b0240282dec55da5b75ac51b7db.png">

设<img src="https://tihai-oss-cloud.itihey.com/img/1afd950894fce4fe04bcb3d3b9f86ede.png">为来自总体<img src="https://tihai-oss-cloud.itihey.com/img/e22a13f7edcffe98b7a922d3fe5be3b8.png">的样本,且<img src="https://tihai-oss-cloud.itihey.com/img/27344b8e07cd0ec70cf8c3ddf911aefa.png">、<img src="https://tihai-oss-cloud.itihey.com/img/c0fb24aea867ce70298a70474708d376.png">均未知,则( )是<img src="https://tihai-oss-cloud.itihey.com/img/2107390c4d3868215a99042d7cbc888a.png">的无偏估计

A. <img src="https://tihai-oss-cloud.itihey.com/img/335a22d904050e2f1f78f467845d3d92.png">B. <img src="https://tihai-oss-cloud.itihey.com/img/8b60b0d78d86624ecb1edd7ccb206bbe.png">C. <img src="https://tihai-oss-cloud.itihey.com/img/2115844725553d8453c4addce9a2d901.png">D. <img src="https://tihai-oss-cloud.itihey.com/img/cf97d5c97e54dfa737388e5f8a9d67c8.png">

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