问题 问答题

设随机变量X与Y相互独立,X的概率分布为PX=i=

(i=-1,0,1),Y的概率密度


(Ⅰ)求


(Ⅱ)求Z的概率密度fz(Z).

答案

参考答案:[分析与解答] (Ⅰ)


由于X,Y相互独立,且y在[0,1)上均匀,故




(Ⅱ)Fz(z)=P{Z≤z)一P{X+Y≤z).可以把“X=-1”,“X=0”和“X=1”看成是一个完备事件组,用全概率公式:




[评注]①本题主要考查条件概率和独立性的运用,关键在于


②一般地说,如果Z=X+Y,其中一个是离散型随机变量,另一个是连续型随饥变量,又相互独立,常常采用本题所用的方法求解.

阅读理解

阅读理解。

     Scientists say illegal logging is threatening one of Mexico's most famous insects. Satellite pictures show

large wooded areas have been cleared from the central Mexican state of Michoacan. The forests are the winter

home for millions of monarch butterflies. The butterflies go there each year to reproduce. After reproducing,

the adult butterflies die, but their young return to the home of their parents each spring.

     The American space agency released the relevant satellite pictures last month. The images show the Monarch

Butterfly Biosphere Reserve. A Mexican law protects trees growing in the area. The images show that about

four hundred and forty-five hectares have been cleared since 2004. Scientists say that, if the clearing continues,

monarch butterflies are unlikely to continue using the Reserve as their winter home.

     For thousands of years, the butterflies have been flying to the same forests. Their trip begins along the border

of Canada and the northeastern United States. The insects fly about eighty kilometers a day. They reach central

Mexico after about sixty days. No one is sure why the brightly coloured orange and black butterflies chose these

forests. However, scientists believe the area might offer the right mix of wetness and cool weather to keep the

insects alive through the winter.

     Lincoln Brower is a professor of biology at Sweet Briar College in Virginia. He has been studying monarch

butterflies for fifty-two years. He says they have been migrating along the same path for about ten thousand

years. People in Mexico have compared the arrival of the butterflies to dark cloud-like formations (阵式) filling

the air. The monarchs arrive in such large numbers that they sometimes cover whole trees.

     Mexico's President ordered special protection for the Monarch Butterfly Biosphere Reserve eight years ago.

The Mexican government has struggled to enforce (强制) the order. Although illegal logging has become one

way for poor people to earn money, other Mexicans are fighting to protect the butterflies' home.

1. What would be the BEST title for the text?

A. Illegal Clearing of Forests Threatens Winter Home of Monarch Butterflies

B. The Forests are the Winter Home for Monarch Butterflies

C. Monarch Butterflies Like the Winter Home in the Forests

D. Protecting the Forests Can Protect Monarch Butterflies

2. Why are the forests called the winter home for millions of monarch butterflies? Because each winter

    the butterflies travel there to _____.

A. avoid cold

B. look for food

C. sleep

D. produce young

3. Why did monarch butterflies choose the forest as their winter home?

A. It has many trees.

B. It has the appropriate environment for them.

C. It is easy to get to.

D. We don't know.

4. The underlined word "migrating" in paragraph 4 is closest in meaning to "_____".

A. going to live in another area or country, especially in order to find food

B. travelling regularly from one part of the world to another

C. changing from one place or position to another

D. starting using an area again as a place to live

5. What can be inferred from the last paragraph? 

A. Mexico has nothing but forests.

B. Most people in Mexico are poor.

C. All Mexicans are destroying the butterflies' home.

D. Some poor people in Mexico often break the law.

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