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设为取自正态总体N(u, σ<sup>2</sup>)的一个样本,试求统计量U=的分布,其中是不全为零的常数.
设为取自正态总体N(u, σ<sup>2</sup>)的一个样本,试求统计量U=<img src='https://img2.soutiyun.com/ask/2020-10-04/97067164926978.png' />的分布,其中<img src='https://img2.soutiyun.com/ask/2020-10-04/970671675093257.png' />是不全为零的常数.
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设X<sub>1</sub>, X<sub>2</sub>, ... X<sub>9</sub>是取自正态总体X~N(μ, σ<sup>2)</sup>的样本,且。求证:。
设X<sub>1</sub>, X<sub>2</sub>, ... X<sub>9</sub>是取自正态总体X~N(μ, σ<sup>2)</sup>的样本,且<img src='https://img2.soutiyun.com/ask/2020-08-09/965847636141377.png' />。
求证:<img src='https://img2.soutiyun.com/ask/2020-08-09/965848226531146.png' />。
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已知X<sub>1</sub>,X<sub>2</sub>,…,X<sub>6</sub>是来自正态总体N(0,σ<sup>2</sup>)的简单随机样本.且 求a和n. 解题
已知X<sub>1</sub>,X<sub>2</sub>,…,X<sub>6</sub>是来自正态总体N(0,σ<sup>2</sup>)的简单随机样本.且
<img src='https://img2.soutiyun.com/ask/2020-08-10/96589894787285.png' />
求a和n.
解题提示 根据t分布的定义来求.
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设 为来自总体N(μ,σ2)的简单随机样本, 为样本均值,已知 是σ<sup>2</sup>的无偏估计(或ET=σ<sup>2</sup>),
设<img src='https://img2.soutiyun.com/ask/2020-11-18/974563559946235.png' />为来自总体N(μ,σ2)的简单随机样本,<img src='https://img2.soutiyun.com/ask/2020-11-18/974563569546784.png' />为样本均值,已知<img src='https://img2.soutiyun.com/ask/2020-11-18/974563615737426.png' />是σ<sup>2</sup>的无偏估计(或ET=σ<sup>2</sup>),则常数C必为()
A.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563625160965.png' />
B.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563634424495.png' />
C.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563643532016.png' />
D.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563651352464.png' />
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设X<sub>1</sub>,X<sub>2</sub>,...,X<sub>n</sub>是取自正态总体N(μ,σ<sup>2</sup>)的样本,μ与σ均未知,则σ<sup>2</sup>的矩估
设X<sub>1</sub>,X<sub>2</sub>,...,X<sub>n</sub>是取自正态总体N(μ,σ<sup>2</sup>)的样本,μ与σ均未知,则σ<sup>2</sup>的矩估计量<img src='https://img2.soutiyun.com/ask/2021-01-05/978692195864823.jpg' />为()。
<img src='https://img2.soutiyun.com/ask/2021-01-05/978692212468773.jpg' />
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设(X<sub>1</sub>,X<sub>2</sub>,…,X<sub>17</sub>)是来自正态分布N(μ,σ<sup>2</sup>)的一个样本,与S<sup>2</sup>分别是样本均
设(X<sub>1</sub>,X<sub>2</sub>,…,X<sub>17</sub>)是来自正态分布N(μ,σ<sup>2</sup>)的一个样本,<img src='https://img2.soutiyun.com/ask/2020-09-17/969203692407925.png' />与S<sup>2</sup>分别是样本均值与样本方差,求k,使得P{<img src='https://img2.soutiyun.com/ask/2020-09-17/969203707825806.png' />>μ+kS}=0.95.
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设为取自总体X的一个样本,总体X~N(μ, σ<sup>2</sup>),分别为样本均值和样本方差,求常数k使得。
设<img src='https://img2.soutiyun.com/ask/2020-10-04/970676527118777.png' />为取自总体X的一个样本,总体X~N(μ, σ<sup>2</sup>),<img src='https://img2.soutiyun.com/ask/2020-10-04/970676548305989.png' />分别为样本均值和样本方差,求常数k使得<img src='https://img2.soutiyun.com/ask/2020-10-04/970676562899824.png' />。
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设X<sub>1</sub>,X<sub>2</sub>,...X<sub>20</sub>是来自正态总体N(0,0.3<sup>2</sup>)的一个样本,求:
设X<sub>1</sub>,X<sub>2</sub>,...X<sub>20</sub>是来自正态总体N(0,0.3<sup>2</sup>)的一个样本,求:
<img src='https://img2.soutiyun.com/ask/2020-07-31/965060656688145.png' />
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设X<sub>1</sub>,X<sub>2</sub>,...X<sub>n</sub>(n≥2)为来自正态总体N(0,1)的简单随机样本,为样本均值,S<sup>2</sup>为样
设X<sub>1</sub>,X<sub>2</sub>,...X<sub>n</sub>(n≥2)为来自正态总体N(0,1)的简单随机样本,<img src='https://img2.soutiyun.com/ask/2020-07-31/965062468168756.png' />为样本均值,S<sup>2</sup>为样本方差,则正确的是()。
<img src='https://img2.soutiyun.com/ask/2020-07-31/965062477119268.png' />
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设总体X服从正态分布N(μ,σ<sup>2</sup>)(σ>0).从该总体中抽取简单随机样本 ,其样本均值为 求统计量
设总体X服从正态分布N(μ,σ<sup>2</sup>)(σ>0).从该总体中抽取简单随机样本<img src='https://img2.soutiyun.com/ask/2020-11-18/974556174244797.png' />,其样本均值为<img src='https://img2.soutiyun.com/ask/2020-11-18/974556183114305.png' />求统计量<img src='https://img2.soutiyun.com/ask/2020-11-18/974556216981242.png' />的数学期望EY.
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设是取自正态总体N(0,σ<sup>2</sup>)的一个样本,求下列统计量的抽样分布:
设<img src='https://img2.soutiyun.com/ask/2020-10-04/970675604977034.png' />是取自正态总体N(0,σ<sup>2</sup>)的一个样本,求下列统计量的抽样分布:
<img src='https://img2.soutiyun.com/ask/2020-10-04/970675639287996.png' />
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设样本X<sub>1</sub>,X<sub>2</sub>,...,X<sub>n</sub>取自正态总体N(μ,σ<sub>0</sub><sup>2</sup>)(σ<sub>0</sub><sup>2</sup>已知),对检验假
设样本X<sub>1</sub>,X<sub>2</sub>,...,X<sub>n</sub>取自正态总体N(μ,σ<sub>0</sub><sup>2</sup>)(σ<sub>0</sub><sup>2</sup>已知),对检验假设H<sub>0</sub>:μ=μ<sub>0</sub>,H<sub>1</sub>:μ>μ<sub>0</sub>的问题,取拒绝域<img src='https://img2.soutiyun.com/ask/2020-12-30/978192934116923.jpg' />
(1)求此检验犯第一类错误的概率为a时,犯第二类错误的概率β,并讨论它们之间的关系;
(2)设μ<sub>0</sub>=0.5,σ<sub>0</sub><sup>2</sup>=0.04,α=0.05,n=9,求μ=0.65时不犯第二类错误的概率。
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设χ<sub>1</sub>,χ<sub>2</sub>,…,χ<sub>n</sub>是来自正态总体N(μ,σ<sup>2</sup>)的一个样本,求参数μ,σ<sup>2</sup>的矩估计量.
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设 是来自总体X~N(μ,σ<sup>2</sup>)的样本,其中μ已知,σ<sup>2</sup>>0为未知参数,样本均值为 ,则σ<sup>2</sup>
设<img src='https://img2.soutiyun.com/ask/2020-11-18/974563559946235.png' />是来自总体X~N(μ,σ<sup>2</sup>)的样本,其中μ已知,σ<sup>2</sup>>0为未知参数,样本均值为<img src='https://img2.soutiyun.com/ask/2020-11-18/974563569546784.png' />,则σ<sup>2</sup>的最大似然估计量为()
A.<img src='https://img2.soutiyun.com/ask/2020-11-18/97456369359988.png' />
B.<img src='https://img2.soutiyun.com/ask/2020-11-18/97456370198636.png' />
C.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563711307893.png' />
D.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563720210402.png' />
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测定某种溶液中的水分,它的10个测定值给出s=0.037%。设测定值总体服从正态分布,σ<sup>2</sup>为总体方差,σ<sup>2</sup>未知,试在a=0.05的水平下检验假设。
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设总体X服从正态分布N(μ, σ<sup>2</sup>) (σ>0),从总体中抽取简单随机样本,其样本均值为求统计量的
设总体X服从正态分布N(μ, σ<sup>2</sup>) (σ>0),从总体中抽取简单随机样本<img src='https://img2.soutiyun.com/ask/2020-08-09/965846856163765.png' />,其样本均值为<img src='https://img2.soutiyun.com/ask/2020-08-09/965846906898667.png' />求统计量<img src='https://img2.soutiyun.com/ask/2020-08-09/965846894326948.png' /><img src='https://img2.soutiyun.com/ask/2020-08-09/965846932984159.png' />的数学期望。
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设X<sub>1</sub>,X<sub>2</sub>,...,X<sub>15</sub>是来自正态总体X~N(0,2<sup>2</sup>)的样本,记,求Y的分布。
设X<sub>1</sub>,X<sub>2</sub>,...,X<sub>15</sub>是来自正态总体X~N(0,2<sup>2</sup>)的样本,记<img src='https://img2.soutiyun.com/ask/2020-11-26/97524949946665.jpg' />,求Y的分布。
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测定某种溶液中的水分,它是10个测定值给出s=0.037%,设测定值总体服从正态分布,σ<sup>2</sup>为总体方差,σ<sup>2</sup>未知,试在α=0.05水平下检验假设:H<sub>0</sub>:σ≥0.04%,H<sub>1</sub>:σ<sub></sub><0.04%。
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设总体X~N(0,σ<sup>2</sup>),X<sub>1</sub>,X<sub>2</sub>,...,X<sub>n</sub>是来自总体X的一个样本.
设总体X~N(0,σ<sup>2</sup>),X<sub>1</sub>,X<sub>2</sub>,...,X<sub>n</sub>是来自总体X的一个样本.
<img src='https://img2.soutiyun.com/ask/2020-09-30/970341001201029.png' />
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设两个正态分布总体X~N(μ<sub>1</sub>,σ<sup>2</sup><sub>1</sub>),Y~N(μ<sub>2</sub>,σ<sup>2</sup><sub>2</sub>),X<sub>1</sub>,X<sub>2</sub>,...
设两个正态分布总体X~N(μ<sub>1</sub>,σ<sup>2</sup><sub>1</sub>),Y~N(μ<sub>2</sub>,σ<sup>2</sup><sub>2</sub>),X<sub>1</sub>,X<sub>2</sub>,...,X<sub>m</sub>与Y<sub>1</sub>,...,Y<sub>n</sub>是分别来自相互独立的总体X与Y的简单随机样本,S<sup>2</sup><sub>1</sub>与S<sup>2</sup><sub>2</sub>分别是其样本方差,已知m=8,S<sup>2</sup><sub>1</sub>=8.75,n=10,S<sup>2</sup><sub>2</sub>=2.66,求P{σ<sup>2</sup><sub>1</sub><σ<sup>2</sup><sub>2</sub>).
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设 ,是来自总体N(0,σ<sup>2</sup>)的简单随机样本,则可以构造未知参数σ<sup>2</sup>的无偏估计量(或数学
设<img src='https://img2.soutiyun.com/ask/2020-11-18/974562941547865.png' />,是来自总体N(0,σ<sup>2</sup>)的简单随机样本,则可以构造未知参数σ<sup>2</sup>的无偏估计量(或数学期望为σ<sup>2</sup>的统计量)()
A.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563028033812.png' />
B.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563036905319.png' />
C.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563044501754.png' />
D.<img src='https://img2.soutiyun.com/ask/2020-11-18/974563052164192.png' />
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设X<sub>1</sub>,X<sub>2</sub>,…,X<sub>n</sub>是来自正态总体N(μ,σ<sup>2</sup>)的简单随机样本,记i=1,2,...,n.求Y<sub>i⌘
设X<sub>1</sub>,X<sub>2</sub>,…,X<sub>n</sub>是来自正态总体N(μ,σ<sup>2</sup>)的简单随机样本,记
<img src='https://img2.soutiyun.com/ask/2020-08-10/965898914993969.png' />i=1,2,...,n.求Y<sub>i</sub>服从的分布及相应的概率密度函数.
解题提示 相互独立的正态分布的随机变量的线性组合仍服从正态分布.
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设 为来自总体N(μ,σ<sup>2</sup>)(σ>0)的简单随机样本;令 则()A.B.C.D.
设<img src='https://img2.soutiyun.com/ask/2020-11-18/974555447058205.png' />为来自总体N(μ,σ<sup>2</sup>)(σ>0)的简单随机样本;令<img src='https://img2.soutiyun.com/ask/2020-11-18/974555483547292.png' />则()
A.<img src='https://img2.soutiyun.com/ask/2020-11-18/974555514524064.png' />
B.<img src='https://img2.soutiyun.com/ask/2020-11-18/974555523007549.png' />
C.<img src='https://img2.soutiyun.com/ask/2020-11-18/974555531280022.png' />
D.<img src='https://img2.soutiyun.com/ask/2020-11-18/974555539864513.png' />
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设X<sub>1</sub>,X<sub>2</sub>,...,X<sub>9</sub>是来自正态总体X~N(0,2<sup>2</sup>)的样本,求a,b,c使得:
设X<sub>1</sub>,X<sub>2</sub>,...,X<sub>9</sub>是来自正态总体X~N(0,2<sup>2</sup>)的样本,求a,b,c使得:<img src='https://img2.soutiyun.com/ask/2020-11-26/975249407058365.jpg' />