设总体X~U<0.θ).其中未知参数θ>0。为来自总体X的一个简单随机样本,求θ的矩估计量和最大似然估计

A . 正确 B . 错误

设总体密度函数为<img src='https://img2.soutiyun.com/ask/2020-09-17/969213726752856.jpg' />,x＞0,θ＞0,求日的费希尔信息量I(θ).

设<img src='https://img2.soutiyun.com/ask/2020-11-18/974564391566801.png' />是来自总体X的简单随机样本，已知X~E(λ),其中λ＞0是未知参数,试求 (I)λ的矩估计量<img src='https://img2.soutiyun.com/ask/2020-11-18/974564415083146.png' /> (II)λ的最大似然估计量<img src='https://img2.soutiyun.com/ask/2020-11-18/974564423164609.png' />

设总体X服从[-θ,θ]上的均匀分布,其中θ(θ>0)为未知参数，<img src='https://img2.soutiyun.com/ask/2020-07-27/964695089964574.png' />是来自总体的简单随机样本. (1)求θ的矩估计量<img src='https://img2.soutiyun.com/ask/2020-07-27/964695055661612.png' />;(2)求θ的最大似然估计量<img src='https://img2.soutiyun.com/ask/2020-07-27/964695070951486.png' />.

设<img src='https://img2.soutiyun.com/ask/2020-10-04/970677629200813.png' />是取自总体X的一个样本，X的分布函数为<img src='https://img2.soutiyun.com/ask/2020-10-04/970677646302791.png' />，其中θ未知，θ＞0.试求θ的极大似然估计量.

A．4.935 B．1.645 C．3.29 D．2u

设<img src='https://img2.soutiyun.com/ask/2020-11-18/974563559946235.png' />是来自总体X~N(μ,σ²)的样本,其中μ已知,σ²＞0为未知参数,样本均值为<img src='https://img2.soutiyun.com/ask/2020-11-18/974563569546784.png' />,则σ²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' />

设随机变量X服从参数为λ的指数分布.当k<x《k+1时。y=k，k=0,1... (1)求Y的分布律 (2)设<img src='https://img2.soutiyun.com/ask/2020-07-27/964694825159428.png' />为来自总体Y的简单随机样本<img src='https://img2.soutiyun.com/ask/2020-07-27/964694844701546.png' />,求λ的矩估计量<img src='https://img2.soutiyun.com/ask/2020-07-27/964694861018479.png' />和最大似然估计量<img src='https://img2.soutiyun.com/ask/2020-07-27/96469488166266.png' />

设总体X服从参数为P的0-1分布,则来自总体X的简单随机样本<img src='https://img2.soutiyun.com/ask/2020-11-18/974554990191073.png' />的概率分布为___

设X₁，X₂，...，X_n是来自总体X的一个样本，<img src='https://img2.soutiyun.com/ask/2020-07-31/965065517141147.png' />而X的概率密度函数为<img src='https://img2.soutiyun.com/ask/2020-07-31/965065529339845.png' />其中θ＞0是未知参数.(1)求总体X的分布函数F(x);(2)求统计量<img src='https://img2.soutiyun.com/ask/2020-07-31/9650655477839.png' />的分布函数<img src='https://img2.soutiyun.com/ask/2020-07-31/965065558561516.png' />;(3)判断<img src='https://img2.soutiyun.com/ask/2020-07-31/965065567199011.png' />是否为θ的无偏估计量。

B、θ的极大似然估计值是0.7 C、θ的矩估计值是0.6 D、θ的极大似然估计值是0.5 E、θ的矩估计值是0 F、θ的极大似然估计值是0.6

A．1/4 B．1/2 C．2 D．0

设X1，…，Xn是来自均匀分布U(0，θ)的样本，θ的先验分布是帕雷托(Pareto)分布，密度函数为<img src='https://img2.soutiyun.com/ask/2020-08-04/965408611002708.png' />其中β，θ₀是两个已知的常数. (1)验证：帕雷托分布是θ的共轭先验分布; (2)求θ的贝叶斯估计.

设总体X的一个样本为(X₁,X₂,...,X_n),X的分布密度为 <img src='https://img2.soutiyun.com/ask/2020-10-06/970839014948484.jpg' /> 参数θ＞0未知.(1)求0的矩估计量;(2)求矩估计量的方差;(3)求0的最大似然估计量.

设<img src='https://img2.soutiyun.com/ask/2020-11-18/974562941547865.png' />,是来自总体N(0,σ²)的简单随机样本,则可以构造未知参数σ²的无偏估计量(或数学期望为σ²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' />

设X₁，…，X₆是来自(0，θ)内均匀分布的样本，θ＞0未知。 (1)写出样本的联合密度函数； (2)指出下列样本函数中哪些是统计量，哪些不是？为什么？ <img src='https://img2.soutiyun.com/ask/2020-11-25/97517218125654.jpg' /> (3)设样本的一组观察值是：0.5，1，0.7，0.6，1，1，写出样本均值、样本方差和标准差。

设总体X的密度函数为其<img src='https://img2.soutiyun.com/ask/2020-08-04/965410352488315.png' />中λ＞0为未知参数X₁，…，X_n为抽自此总体的简单随机样本，求λ的置信水平为1-α的置信区间.