一个随机样本来自正态总体x，总体标准差σ=1．5，抽样前希望有95％的置信水平使得μ的估计的置信区间长度为L=1．7，试问应抽取多大的一个样本？

A . ['['1.96σB . 1.96https://assets.asklib.com/psource/2015110815170653471.jpg C .https://assets.asklib.com/psource/2015110815171316604.jpg D .https://assets.asklib.com/psource/2015110815171948972.jpg E . 1.96s

A . A B . B C . C D . D E . E

A . ['['X1-X2+X3B . 2X3-μC .https://assets.asklib.com/psource/2015101517580884933.jpg D .https://assets.asklib.com/psource/2015101517581233582.jpg E .https://assets.asklib.com/psource/2015101517581652360.jpg

A . A B . B C . C D . D

A . A B . B C . C D . D

A . ['['1.96σB . 1.96σhttps://assets.asklib.com/psource/2015092914183963979.gif C .https://assets.asklib.com/psource/2015092914185355064.gif D .https://assets.asklib.com/psource/2015092914185642036.gif E . 2.58σ

已知X₁,X₂,…,X₆是来自正态总体N(0,σ²)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.

设X₁，X₂，...X_n(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，S²为样本方差，则正确的是()。 <img src='https://img2.soutiyun.com/ask/2020-07-31/965062477119268.png' />

如图所示，设总体<img src='https://img2.soutiyun.com/ask/2020-07-27/96469314696044.png' />为来自总体X的一个简单随机样本.<img src='https://img2.soutiyun.com/ask/2020-07-27/9646931619863.png' />分别为其样本均值和样本方差. (1)证明对任意<img src='https://img2.soutiyun.com/ask/2020-07-27/964693245155057.jpg' />的常数的期望为σ²; (2)求常数c,使得<img src='https://img2.soutiyun.com/ask/2020-07-27/964693265241206.png' />达到最小值.

设总体X服从正态分布N(μ，σ²)(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.

设(X₁,X₂,...,X₁₅)是来自正态总体N(0,9)的简单随机样本,则统计量Y<img src='https://img2.soutiyun.com/ask/2020-10-05/9707790061243.jpg' />的概率分布是参数为()的()分布.

设总体X服从正态分布N(μ, σ²) (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。

设总体X~N(0,σ²),X₁,X₂,...,X_n是来自总体X的一个样本. <img src='https://img2.soutiyun.com/ask/2020-09-30/970341001201029.png' />

设X₁，…，X_n为抽自正态总体N(μ，σ²)的简单随机样本，试证 <img src='https://img2.soutiyun.com/ask/2020-08-04/965410591189968.png' /> 为枢轴量，其中k为已知常数，

设X₁,X₂,…,X_n是来自正态总体N(μ,σ²)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_i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.

设总体X~N(01),X1、X2、X3、X4..X5为来自总体X的简单随机样本，<img src='https://img2.soutiyun.com/ask/2020-07-27/964689261739219.png' />分别为样本均值和样本标准差,则下列结论中正确的为()。 A.<img src='https://img2.soutiyun.com/ask/2020-07-27/964689251838652.png' /> B.<img src='https://img2.soutiyun.com/ask/2020-07-27/964689275003977.png' /> C.<img src='https://img2.soutiyun.com/ask/2020-07-27/964689286002606.png' /> D.<img src='https://img2.soutiyun.com/ask/2020-07-27/964689292953004.png' />

设<img src='https://img2.soutiyun.com/ask/2020-11-18/974556800064592.png' />为来自正态总体N(0,σ²)的简单随机样本,则统计量<img src='https://img2.soutiyun.com/ask/2020-11-18/974556809002103.png' />服从的分布为（） A.F(1,1) B.F(2,1) C.t(1) D.t(2)

A．Z检验 B．T检验 C．X检验 D．F检验