问题 问答题

设随机变量X与Y相互独立,且都在[0,1]上服从均匀分布,试求:
1.U=XY的概率密度fU(u);

答案

参考答案:由于X与Y相互独立且密度函数已知,因此我们可以用两种方法:分布函数法与公式法求出U、V的概率密度.
方法1° 分布函数法.由题设知(X,Y)联合概率密度


所以U=XY的分布函数


当u≤0时,FU(u)=0;当u≥1时,FU(u)=1;当0<u<1时,



综上得



方法2° 公式法.已知

X与Y独立,由独立乘积概率密度公式得


由fY(y)表达式知,

,即0<u<x<1时,

,否则

,故当0<u<1时,令

,则


所以

阅读理解

阅读理解。

     Li Daiyu and her cousin Liu Qian were on a trip to Canada to visit their cousins on the Atlantic coast.

Rather than take the aeroplane all the way, they decided to fly from China to Vancouver and to take the

train from west to east across Canada in September.The idea that they would cross the whole continent

was exciting.

     Their friend, Danny Lin,was waiting for them at the airport. He was going to take them to catch 'The

True North', the cross-Canada train.On the way to the station, he told them, 'You're going to see great

scenery on your trip. Canada is bigger than the United States. It is second biggest country in the world

and as you go eastward, you will see mountains and pass thousands of lakes,forests and wide rivers as

well as cities.The idea that you can cross Canada in less than five days is just wrong. It is 5,500

kilometres from coast to coast.Here in Vancouver,you are in the warmest part of Canada.Many people

think it is the most beautiful city in Canada,as it is surrounded by mountains on the north and east and the

Pacific Ocean on the west.Its population is increasing very rapidly, because the mountain-and-sea city is

a very popular place to live in.Even people from Japan come to settle down here.

     That afternoon on the train the cousins settled down in their seats. They crossed the Rocky Mountains

earlier that day and looked out of the windows at the wild scencry.They saw mountain goats and even a

grizzly bear.Their next stop would be Calgary.The Calgary Stampede is a famous Western festival,

Cowboys come from all over North America to compete in riding wild horses.Many of them have a gift

for working with animals and they can win thousands of dollars in prizes.

     That night,they slept as the train rushed through the night across the top of Lake Superior.through the

great forests and southward towards Toronto.

1. How did Li Daiyu and Liu Qian arrive in Canada?

A. They sailed across the Pacific Ocean.        

B. They flew to Vancouver.

C. They took a train to Vancouver.              

D.  They flew to the Atlantic coast.

2. Witch order is right of their train trip?

A. Vancouver  Calgary   Lake Superior  Toronto

B. Toronto   Vancouver  Calgary   Lvake Superior

C. Vancouver  Lake Superior   Calgary   Toronto

D. Lake Superior    Vancouver   Cvalgary   Tvoronto

单项选择题