【单选题】
设总体<img class=jc-formula data-tex=X src=https://huaweicloudobs.ahjxjy.cn/18E2773B1E2835B209E7E51B85285E80.png style=vertical-align: middle;/>的数学期望为<img class=jc-formula data-tex=\mu , src=https://huaweicloudobs.ahjxjy.cn/07393889DE1E04D799FC2171DD4841CF.png style=vertical-align: middle;/><img class=jc-formula data-tex={ X }_{ 1 },{ X }_{ 2 },\cdots { X }_{ n } src=https://huaweicloudobs.ahjxjy.cn/7872682357A677F5C3693835FBDE154B.png style=vertical-align: middle;/>为来自<img class=jc-formula data-tex=X src=https://huaweicloudobs.ahjxjy.cn/18E2773B1E2835B209E7E51B85285E80.png style=font-family: 宋体; font-size: 14px; line-height: 24px; white-space: normal; vertical-align: middle;/>的样本,则下列结论中正确的是
①
<img class=jc-formula data-tex={ X }_{ 1 } src=https://huaweicloudobs.ahjxjy.cn/DA66F1A424E4031AEED284B5B6FE9A43.png style=vertical-align: middle;/>是<img class=jc-formula data-tex=\mu \quad src=https://huaweicloudobs.ahjxjy.cn/72143C62DAAAA39AB69A5506838561CA.png style=vertical-align: middle;/>的无偏估计量
②
<img class=jc-formula data-tex={ X }_{ 1 } src=https://huaweicloudobs.ahjxjy.cn/DA66F1A424E4031AEED284B5B6FE9A43.png style=white-space: normal; vertical-align: middle;/>是<img class=jc-formula data-tex=\mu \quad src=https://huaweicloudobs.ahjxjy.cn/72143C62DAAAA39AB69A5506838561CA.png style=font-family: 宋体; font-size: 14px; white-space: normal; vertical-align: middle;/>的极大似然估计量
③
<img class=jc-formula data-tex={ X }_{ 1 } src=https://huaweicloudobs.ahjxjy.cn/DA66F1A424E4031AEED284B5B6FE9A43.png style=white-space: normal; vertical-align: middle;/>是<img class=jc-formula data-tex=\mu \quad src=https://huaweicloudobs.ahjxjy.cn/72143C62DAAAA39AB69A5506838561CA.png style=font-family: 宋体; font-size: 14px; white-space: normal; vertical-align: middle;/>的相合(一致)估计量
④
<img class=jc-formula data-tex={ X }_{ 1 } src=https://huaweicloudobs.ahjxjy.cn/DA66F1A424E4031AEED284B5B6FE9A43.png style=white-space: normal; vertical-align: middle;/>不是<img class=jc-formula data-tex=\mu \quad src=https://huaweicloudobs.ahjxjy.cn/72143C62DAAAA39AB69A5506838561CA.png style=font-family: 宋体; font-size: 14px; white-space: normal; vertical-align: middle;/>的估计量
【单选题】
设A,B为两随机事件,且A<img class=jc-formula data-tex=\supset src=https://huaweicloudobs.ahjxjy.cn/37A4B3C430EFA04CF480D02C0DFECE89.png style=vertical-align: middle; width: 20px; height: 17px; width=20 height=17/>B,则下列式子正确的是
①
P(A<img class=jc-formula data-tex=\cup src=https://huaweicloudobs.ahjxjy.cn/9BD598E68F21E65385221B2250659C3A.png style=vertical-align: middle; width: 22px; height: 14px; width=22 height=14/>B) = P(A)
②
P(AB)=P(A)<img width=99 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/>
④
P(B-A)=P(B)-P(A)<img width=76 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=83 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=76 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=83 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=76 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=83 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=76 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=83 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=76 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/><img width=83 height=21 src=http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/spacer.gif word_img=file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif style=background:url(http://www.ahjxjy.cn/design/html/js/vender/ueditor/themes/default/images/word.gif) no-repeat center center;border:1px solid #ddd/>
【单选题】
设A、B为随机事件,且<img class=jc-formula data-tex=A\subset B src=https://huaweicloudobs.ahjxjy.cn/C33E9654307A887E880041F3D601FD97.png style=vertical-align: middle;/>,则<img class=jc-formula data-tex=\overline { A\cup B } src=https://huaweicloudobs.ahjxjy.cn/79477E4BD1EEACFFEB3601D898572A40.png style=vertical-align: middle;/>=( )
①
<img src=https://huaweicloudobs.ahjxjy.cn/7D3B24BFF7FB07A1ACBD45082E10AEE3.png style=vertical-align: middle;/>
②
<img src=https://huaweicloudobs.ahjxjy.cn/CCA6902D31F21EE44E3B8F5DC1598331.png style=vertical-align: middle;/>
③
<img src=https://huaweicloudobs.ahjxjy.cn/79B6F461016024364313203B75308D7A.png style=vertical-align: middle;/>
④
<img src=https://huaweicloudobs.ahjxjy.cn/F0FB0756B4646ADDC3EA900C9EA02F0F.png style=vertical-align: middle;/>
【单选题】
设<img class=jc-formula data-tex={ X }_{ 1 },\cdots ,{ X }_{ n } src=https://huaweicloudobs.ahjxjy.cn/8159F7186DE77C735294288BB1F8C1F1.png style=vertical-align: middle;/>是来自总体<img class=jc-formula data-tex=X src=https://huaweicloudobs.ahjxjy.cn/18E2773B1E2835B209E7E51B85285E80.png style=vertical-align: middle;/>的样本,且<img class=jc-formula data-tex=EX=\mu src=https://huaweicloudobs.ahjxjy.cn/39618736AA44811087C44938D156DBC3.png style=vertical-align: middle;/>,则下列是<img class=jc-formula data-tex=\mu src=https://huaweicloudobs.ahjxjy.cn/44B6A27E434C1345C3CEEB7A5249665D.png style=vertical-align: middle;/>的无偏估计的是
①
<img class=jc-formula data-tex=\frac { 1 }{ n } \sum _{ i=1 }^{ n-1 }{ { X }_{ i } } src=https://huaweicloudobs.ahjxjy.cn/C47B85208815D85D3DD90DFEC473F7FF.png style=vertical-align: middle;/>
②
<img class=jc-formula data-tex=\frac { 1 }{ n-1 } \sum _{ i=1 }^{ n }{ { X }_{ i } } src=https://huaweicloudobs.ahjxjy.cn/F592094A4BE03E45216F0FE940311E37.png style=vertical-align: middle;/>
③
<img class=jc-formula data-tex=\frac { 1 }{ n } \sum _{ i=2 }^{ n }{ { X }_{ i } } src=https://huaweicloudobs.ahjxjy.cn/72F0F6F417A0E32959CC0BA9BC395311.png style=vertical-align: middle;/>
④
<img class=jc-formula data-tex=\frac { 1 }{ n-1 } \sum _{ i=1 }^{ n-1 }{ { X }_{ i } } src=https://huaweicloudobs.ahjxjy.cn/1C176141AB6A855E8CFD52AEF5D595C0.png style=vertical-align: middle;/>
【单选题】
若X~t(n),那么<img class=jc-formula data-tex={ \chi }^{ 2 }\~ src=https://huaweicloudobs.ahjxjy.cn/7524F79C96AF5A4818C61A2714F65EA8.png style=vertical-align: middle; width: 37px; height: 21px; width=37 height=21/>
①
<img class=jc-formula data-tex=F(1,n) src=https://huaweicloudobs.ahjxjy.cn/25C501008EFE85191DEADAF449F2956D.png style=vertical-align: middle;/>
②
<img class=jc-formula data-tex=F(n,1) src=https://huaweicloudobs.ahjxjy.cn/42BA09551C47FD15676968790AA60E46.png style=vertical-align: middle;/>
③
<img class=jc-formula data-tex={ \chi }^{ 2 }(n) src=https://huaweicloudobs.ahjxjy.cn/82A4224D6B4F6EE7FE7625A4AC6E18B9.png style=vertical-align: middle;/>
④
<img class=jc-formula data-tex=t(n) src=https://huaweicloudobs.ahjxjy.cn/4CD969C45CFD16EEE09EF62D4D7DB5BB.png style=vertical-align: middle;/>
【多选题】
关于正态分布<img class=jc-formula data-tex=N(\mu ,{ \sigma }^{ 2 }) src=https://huaweicloudobs.ahjxjy.cn/CAA65D1EC6C1DBEDB20A490E6E422BA0.png style=vertical-align: middle; width: 77px; height: 29px; width=77 height=29/>,下列正确的是
①
<img class=jc-formula data-tex=P(X\le \mu )=\frac { 1 }{ 2 } src=https://huaweicloudobs.ahjxjy.cn/8D0D906A45C5F856FBB82E3CC91F2BA4.png style=vertical-align: middle;/>
②
<img class=jc-formula data-tex=\frac { X-\mu }{ \sigma } \~ N(0,1) src=https://huaweicloudobs.ahjxjy.cn/68E9F7BE2936505CACBBA73F433FFC91.png style=vertical-align: middle;/>
③
<img class=jc-formula data-tex=\mu 一定时,\sigma 越小,其概率密度函数图形越陡。 src=https://huaweicloudobs.ahjxjy.cn/9303FE8C0038493E66620B7961A939B3.png style=vertical-align: middle;/>
④
<img class=jc-formula data-tex=\mu 一定时,\sigma 越大,其概率密度函数图形越陡。 src=https://huaweicloudobs.ahjxjy.cn/B19ACA96F69602C3A83F1FD22048D322.png style=vertical-align: middle;/>
【单选题】
已知随机变量X的密度函数<img class=jc-formula data-tex=f(x)=\begin{ cases } A{ e }^{ -x },x\ge \lambda \\ 0,\quad x\lambda \end{ cases }(\lambda 0,A src=https://huaweicloudobs.ahjxjy.cn/170AA0E56CF07A9CB01C1277AD5B5B64.png style=vertical-align: middle; width: 138px; height: 38px; width=138 height=38/>为常数),则概率<img class=jc-formula data-tex=P\left\{ \lambda \lambda +a \right\} (a0) src=https://huaweicloudobs.ahjxjy.cn/414D170A5B5901D4BDB55E9237201D47.png style=vertical-align: middle; width: 142px; height: 22px; width=142 height=22/>的值
①
与a无关,随<img class=jc-formula data-tex=\lambda src=https://huaweicloudobs.ahjxjy.cn/14C3B57DF5E84C1472D22AC460DC2BA0.png style=vertical-align: middle;/>的增大而增大
②
与a无关,随<img class=jc-formula data-tex=\lambda src=https://huaweicloudobs.ahjxjy.cn/14C3B57DF5E84C1472D22AC460DC2BA0.png style=font-family: 宋体; font-size: 14px; white-space: normal; vertical-align: middle;/>的增大而减小
③
与<img class=jc-formula data-tex=\lambda src=https://huaweicloudobs.ahjxjy.cn/14C3B57DF5E84C1472D22AC460DC2BA0.png style=font-family: 宋体; font-size: 14px; white-space: normal; vertical-align: middle;/>无关,随a的增大而增大
④
与<img class=jc-formula data-tex=\lambda src=https://huaweicloudobs.ahjxjy.cn/14C3B57DF5E84C1472D22AC460DC2BA0.png style=white-space: normal; font-family: 宋体; font-size: 14px; vertical-align: middle;/>无关,随a的增大而减小
【单选题】
表示两事件A,B的“交事件”的是A.<img class=jc-formula data-tex=A\subset B src=https://huaweicloudobs.ahjxjy.cn/C71575BA4DFD20383E7F5C41F8A28934.png style=vertical-align: middle;/>; B.<img class=jc-formula data-tex=A\bigcup B src=https://huaweicloudobs.ahjxjy.cn/982CA6CED9D227756514768C253E1E65.png style=vertical-align: middle;/>; C.<img class=jc-formula data-tex=A\bigcap B src=https://huaweicloudobs.ahjxjy.cn/904886EFF42292411706DCA15D31C87D.png style=vertical-align: middle;/>; D.<img class=jc-formula data-tex=A-B src=https://huaweicloudobs.ahjxjy.cn/E7913F72D5FDBF5C2EF8AE9136291C29.png style=vertical-align: middle;/>
【单选题】
表示两事件A,B的“差事件”的是A.<img class=jc-formula data-tex=A\subset B src=https://huaweicloudobs.ahjxjy.cn/C71575BA4DFD20383E7F5C41F8A28934.png style=vertical-align: middle;/>; B.<img class=jc-formula data-tex=A\bigcup B src=https://huaweicloudobs.ahjxjy.cn/982CA6CED9D227756514768C253E1E65.png style=vertical-align: middle;/>; C.<img class=jc-formula data-tex=A\bigcap B src=https://huaweicloudobs.ahjxjy.cn/904886EFF42292411706DCA15D31C87D.png style=vertical-align: middle;/>; D.<img class=jc-formula data-tex=A-B src=https://huaweicloudobs.ahjxjy.cn/E7913F72D5FDBF5C2EF8AE9136291C29.png style=vertical-align: middle;/>
【单选题】
表示两事件A,B的“和事件”的是A.<img class=jc-formula data-tex=A\subset B src=https://huaweicloudobs.ahjxjy.cn/C71575BA4DFD20383E7F5C41F8A28934.png style=vertical-align: middle;/>; B.<img class=jc-formula data-tex=A\bigcup B src=https://huaweicloudobs.ahjxjy.cn/982CA6CED9D227756514768C253E1E65.png style=vertical-align: middle;/>; C.<img class=jc-formula data-tex=A\bigcap B src=https://huaweicloudobs.ahjxjy.cn/904886EFF42292411706DCA15D31C87D.png style=vertical-align: middle;/>; D.<img class=jc-formula data-tex=A-B src=https://huaweicloudobs.ahjxjy.cn/E7913F72D5FDBF5C2EF8AE9136291C29.png style=vertical-align: middle;/>