问题 问答题

设总体X的概率密度为


其中θ是未知参数(0<θ<1),X1,X2,…,Xn为来自总体X的简单随机样本,记N为样本值x1,x2,…,xn中小于1的个数.求

θ的最大似然估计.

答案

参考答案:用最大似然估计定义求解.
由于样本x1,…,xn的似然函数[*],
取对数得lnL(θ)=Nlnθ+(n-N)ln(1-θ)
令[*],解得θ的最大似然估计为[*].

阅读理解

If Confucius were still alive today and could celebrate his September 28 birthday with a big cake, there would be a lot of candles. He’d need a fan or a strong wind to help him put them out.

While many people in China will remember Confucius on his special day, few people in the United States will give him a passing thought. It’s nothing personal. Most Americans don’t even remember the birthdays of their own national heroes.

But this doesn’t mean that Americans don’t care about Confucius. In many ways he has become a bridge that foreigners must cross if they want to reach a deeper understanding of China.

In the past two decades, the Chinese studies programs have gained huge popularity in Western universities.  More recently, the Chinese government has set up Confucius Institutes in more than 80 countries. These schools teach both Chinese language and culture. The main courses of Chinese culture usually included Chinese art, history and philosophy. Some social scientists suggest that Westerners should take advantages of the ancient Chinese wisdom to make up for the drawbacks of Westerners philosophy. Students in the United States, at the same time, are racing to learn Chinese. So they will be ready for life in a world where China is an equal power with the United States. Businessmen who hope to make money in China are reading books about Confucius to understand their Chinese customers. 

So the old thinker’s ideas are still alive and well.

Today China attracts the West more than ever, and it will need more teachers to introduce Confucius and Chinese culture to the West.

As for the old thinker, he will not soon be forgotten by people in the West, even if his birthday is.

小题1: The opening paragraph is mainly intended to _________.

A.provide some key facts about Confucius

B.attract the readers’ interest in the subject

C.show great respect for the ancient thinker

D.prove the popularity of modern birthday celebrations小题2:We can learn from Paragraph 4 that American students_________.

A.fight for a chance to learn Chinese

B.try to get high scores in Chinese exams

C.have a great interest in studying Chinese

D.take an active part in Chinese competitions小题3: What is the best title for the passage?

A.Forgotten Wisdom in America

B.Old Thinker with a Big Future

C.Chinese Culture for Westerners

D.Huge Fans of the Chinese Language小题4: The passage is likely to appear in _________.

A.a biography

B.a history paper

C.a newspaper

D.a philosophy textbook

单项选择题

  一般认为,南方古猿类可以分为两大类型,即纤细型和粗壮型。年代最早的南方古猿是纤细型,俗名叫“露西”,是1973年美国的约翰逊考察队在埃塞俄比亚的阿法凹地发现的,其年代原先测定为距今370万年前,最近重新测定为340万年前,定名为南方古猿阿法种。距今大约300~250万年之间出现了另一种纤细型南方古猿,定名为南方古猿非洲种,是达特和布鲁姆等在南非发现的。粗壮型南方古猿最早是30年代布鲁姆在南非的一些地点发现的。1959年利基夫妇在东非坦桑尼亚的奥杜韦发现了一具完整的粗壮头骨,命名为南方古猿鲍氏种,其年代为距今大约200万年前。 1985年美国的沃克等在肯尼亚特卡纳湖西岸发现了一个头骨,色泽较深,俗称“黑头骨”。头骨粗壮,与在坦桑尼亚奥杜韦发现的南方古猿鲍氏种相似,但其年代为距今约250万年前,比鲍氏种早了50万年。

  纤细型南方古猿最早出现于近400万年前。这类古猿的形态较为细巧,行动较为敏捷,能适应多种环境和利用多种食物,包括部分肉食,脑子较为发达,智力较高。在距今大约200多万年前发展成为真人,归入人属。

  粗壮型南方古猿最初出现于至少距今250万年前,体形粗壮,其总的性状很少变化,行动较为迟钝,主要以森林边缘粗糙而坚硬的植物种子和块茎为食,在大约100万年前灭绝了,没有能转变成真人。

导致纤细型和粗壮型南方古猿不同结局的最大原因是()

A.一个形态纤细,一个体形粗壮

B.一个动作敏捷,一个行动迟钝

C.一个智力较高,一个头脑愚笨

D.一个适应多种环境,利用多种食物;一个缺少变化,取食单一