问题 解答题

一个袋中有20个大小相同的小球,其中记上0号的有10个,记上n号的有n个(n=1,2,3,4).现从袋中任取一球,用ξ表示所取球的标号.

(1)求ξ的分布列的数学期望和方差;

(2)若η=aξ+b,E(η)=2,D(η)=44,试求a、b的值.

答案

(1)由题设知ξ=0,1,2,3,4,

P(ξ=0)=

10
20
=
1
2

P(ξ=1)=

1
20

P(ξ=2)=

2
20
=
1
10

P(ξ=3)=

3
20

P(ξ=4)=

4
20
=
1
5

∴ξ的分布列为:

ξ01234
P
1
2
1
20
1
10
3
20
1
5
…(3分)

∴Eξ=

1
2
+1×
1
20
+2×
1
10
+3×
3
20
+4×
1
5
=1.5.…(4分)

Dξ=(0-1.5)2×

1
2
+(1-1.5)2×
1
20
+(2-1.5)2×
1
10
+(3-1.5)2×
3
20
+(4-1.5)2×
1
5
=2.75.…(6分)

(2)由η=a2Dξ,得a2×2.75=44,即a=±4,…(8分)

又Eη=aEξ+b,

∴当a=4时,由2=4×1.5+b,得b=-4;

当a=-4时,由2=-4×1.5+b,得b=8.

a=4
b=-4
a=-4
b=8
即为所求.…(12分)

阅读理解

Waller was a liked-by-all fellow full of fun who often went to coffee houses to tell people interesting stories, of which some even brought him some money. One day, asked by an office secretary who told Waller that his boss was a never-seen before serious man and he never even smiled. Waller would tell a most funny story. “Well, sir,” Waller said before he began the story, “What will be given in return of my success?”“$100,”replied the secretary. “I haven’t seen him have a bright face since I worked in his office.”

“Then let’s make it.” Waller went to the man’s table and whispered to him, “Please tell your boss that the funny man Waller’s hen gave birth to a baby.”

Three days later a letter reached Mr. Waller in which were $100 and a piece of yellow paper with the words, “Mr. Waller, you have succeeded—When I repeated your $100-worth sentence, my boss burst into frightening laughter, saying that whoever has managed to make him laugh during the business hours will get dismissed!”

小题1:The secretary asked Waller for a most funny story because he ______.

A.was tired of his boss seriousness

B.tried to please his serious boss with it

C.wanted to improve his working conditions

D.wanted to see his boss' laughing face小题2:Saying "Let's make it," Waller______.

A.was sure of his success

B.thought of nothing but the 100-dollar return

C.knew that his hen had really given a birth to a baby

D.wondered whether he could make the boss smile or not小题3:Which of the following ends is true according to the passage?

A.The boss was never so strict with the secretary from then on.

B.The secretary lost his job in office.

C.The secretary dare not make his boss laugh any longer.

D.Mr.Waller was dismissed at last.小题4:Which sentence can describe the theme of the story?

A.Things Went Opposite to Wishes

B.Satisfying Both Sides

C.Killing Two Birds with One Stone

D.Either Is in His Proper Place

单项选择题