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范文一：大学电路期末考试题
大学电路期末考试题
1( 下列关于电路中参考方向叙述正确的是 ( )
A( 参考方向是为了计算电路的方便而假定的方向。
B( 参考方向一定与实际方向相反。
C( 参考方向一定与实际方向一致。
D( 若某元件的电压与电流参考方向一致，则该元件的电压与电流的实际方
向也一致。
2( 电路如图1所示，则图中I的电流大小为 ( )
A( 0 A B. 0.5 A C.A D. 1.5 A 3( 电路如图2所示，电路中a、b两端间等效电阻R为 ( ) ab
A. 3 Ω B. 4 Ω C. 5 Ω D. 6 Ω 4( 电路如图3所示，m与n点的电位差为 ( )
A. 1 0 V B. 1 1 V C. 1 2 V D. 1 3 V
5( 已知函数波形如图4所示，则用单位阶跃函数描述正确的为
( )。
A(2
B. 2
A 1
大学电路期末考试题
C. 2
D. 2
6( 已知正弦量，则该正弦量所对应的相量可以表示
为 ( )。
A. 5 B. 5 C. 5 D. 7( 已知如图5所示的某单一元件电压、电流分别为，
,
则该元件为( )。
A(电压源 B. 电阻
C. 电感 D. 电容
二、填空题
1(电路如图6所示，则端口ab的开路电压大小为。
2. 电路如图7所示，则端口的等效阻抗R的大小为。 eq
4(一只额定功率为40W的日光灯接到 110V，50Hz的交流电上，其等效电路如图9所示。测得电路上的电流为 A,则该日光灯的功率因数为。 A 2
大学电路期末考试题
5(已知某函数f(t)=3+4, 则该函数通过拉普拉斯变换后的象函数为。 6. 电路如图10所示，电路原来处于稳态，t=0时开关断开，则) 为。 8(耦合电感电路如图12所示，该端口的等效电感大小为。
三、分析计算题 (10分)
电路如图14所示，通过分析和计算求:(1) U的大小;(2)受控源的功率;(3) 受x
控源实际上吸收功率还是发出功率,
四、分析计算题 (10分)
电路如图15所示，开关S原在位置1时电路已达稳定状态，t=0时开关由位置1合向位置2，求t时电感的电流和电压。
五、分析计算题 (12分)
电路如图16所示的正弦稳态电路，已知电源电压U=100V，电容C的大小为A 3
大学电路期末考试题
50，电流表A的读数为0，且电压与电流同相位。 1
请确定: (1)正弦稳态交流电的频率 f 为多少Hz? (2)电流表 A的读数; (3)
变压器的变压比 n 的大小。
六、分析计算题(12分)。
电路如图18所示三相电系统，已知线电压为380V，Z=10。
(1) 在没有连接电容时，请计算三相电的线电流，功率表W的读数和功率1表W的读数。 2
(2) 为了提高功率因数，需要连接电容。如果为了三相电系统的功率因数到1，请计算此时电路的电容C的大小。 1
(3) 在电路连接电容后，功率表W的读数和功率表W的读数各有什么变12化,
七、分析计算题(12分)。
电路如图18所示，已知u= u=4 V, R=4Ω, R=4Ω, L=1H。电路原出s1s212于稳态，t=0时将开关S闭合。
(1)画出运算电路; (2)求t时，电感的电压i(t) 和电压u(t)。 L L
A 4
大学电路期末考试题
八、分析计算题(10分)。
电路如图19所示，当开关S在位置“1”时，毫安表的读数为20mA; 当开关
S在位置“2”时，毫安表的读书为30mA。
则当开关S在位置“3”时，毫安表的的读数是多大,
A 5
大学电路期末考试题
A 6
范文二：大学高数期末考试题
高等数学(上)期中测试题
一 填空题:(每小题 4分,共 32分,要求:写出简答过程,并且把答案填在横线上) 1. 设
1
(1)
, 0() , 0
x x x f x x a
x ?
?
-<>
(, ) -∞+∞上处处连续,则 a =---。
解
()
()1
1110
lim 1lim 1x
x
x x x x e
----
-→→?
?
??-=+-=????
?
?
(
)
lim x x a
a +
→+=, 有连续性有 a
=-1
e
2. 已 知
(3) 2f '=, 则 0
(3) (3) lim 2h f h f h
→--=
。
解 已知
()0
(3) (3)
3lim
2
h f f h f h →--'==
则
(3) (3)
1(3) (3)
lim
lim
22
h h f h f f f h h
h
→→----=-
()
11321
2
2
f '
=-
?=-?=-
3. 函数
() 2cos f x x x =+在 [0, ]2
π
上的最大值为 6
π+
解 令
()12sin 0f x x '=-=得 6
x π
=
(
)
02
6622f
f f ππππ??
??
==
+=
? ???
??
则最大值为 6
π
+
4. 设
5(sin ) 5(1co s )
x t t y t =+??
=-?
, 则
t dy dx
==2
2
t d y dx
==
120
解
()
5s in 0
5
1
c o s t t t d y
d y t d x d x
t
d t
====
=
=+
2
2
t t t d y d d y d x d d
y
d x d x
d x
d x
d t
===?? ?
???? ?
??
=
=
()()()
2
2
c o s 1c o s s in 1c o s 151c o s 20
t t t t
t t =+++=
=
+
5. 设 1(0) x
y x x +
=>,则 y '=
()1ln x
x
x x x ++
解 两边取对数有 ()ln 1ln y x x =
+
两边关于
x 求导得
1ln y x x y
x
'+=+
, 整理后即得结果
6. 设 函 数
()
y y x =由 方 程
cos() 0
x y xy ++=确 定 , 则
dy =
sin 1
1sin y xy dx x xy
--。
解 对方程两边关于
x 求导 得 :
()()1-sin 0y xy y xy ''+?+=
sin 1
1sin y xy y x xy -'=- 则 dy =
s i n 1
1s i n y x y dx x xy
--
7. 曲线
2x
y e
-=在点
(0,1)M 处的曲率 K
=
425
解
20
22x
x x y e
-=='
=-=- 20
44x
x x y e
-==''
==
则
()
(
)3
2
2
2
2
4425
112y k y ''
=
=
=
??'
+
+-??
8. 函数
() x
f x xe
=在
01x =处的二阶泰勒公式为 () f x =
()()
()()
2
3
3321112
6
e
e e e x x x ξ
ξ++-+
-+
-
解 由
()
()()n x
f
x n x e
=+, 代入泰勒公式即得
二.选择题:(每小题 4分,共 32分,每小题的四个选项中只有一个是正确的,要求写出简答过程,并且将答 案对应的选项的字母填入题后括号里) 1. 当
0x →时,下列函数中为无穷小的函数是(D )
。 A.
lg sin x
; B.
1cos
x
; C.
1sin
x
; D.
12
x e
-
。
解 0. lim lg sin x A x →=-∞ 01
. l i m c o x B x →不存在
1. lim sin
x C x
→不存在
2
10
. l i m 0x
x D e
-
→=
2.
设
2
1sin , 0
() 0
, 0
x f x x
x ?≠?
=?
?=?
,则
() f x 在点 0x =处(C
) 。
A. 极限不存在; B. 极限存在,但不连续; C .连续,但不可导; D. 可导。
解
由
()2
1lim
sin
00x f x
→==
则
() f x 在点 0x =处连续
又
()()(
)
2
1sin
00lim
lim
0x x f
x f f x x
→→-
'==-
2
1lim
sin
x x
→=不存在
则
() f x 在点 0x =处不可导
3. 设
arccos sin 2
x
y =,则
1
() 2
y '=(A ) 。
A.
12
-;
B.
2
-
; C.
12
;
D.
2
。
解
12
12
arccos 11
1cos 22
2
x x x y =
=??'
=?
?=-
???
4. 曲线 cos sin x t t y t t
=??=?在 4t π=
处的切线方程是(
B )
。
A.
4
() 84
8y x ππππ-+-
=
-
+;
B.
4() 8
4
8
y x ππππ+-=--+ ;
C.
y x =; D.
y x =-。
解
4
4
4
sin cos 4cos sin 4t t t dy
dy
t t t dx dx
t t t
dt
π
π
π
ππ
=
=
=
++=
=
=
--
则切线方程为 442442y x ππππ??
+-?=-? ?-??
5. 已知函数
2cos x
y e x =+,则 (40)
y
=(A )
。 A.
4022cos x
e
x ?+; B. 40
22
sin x
e
x ?+;
C.
2cos x
e
x +; D. 2sin x
e
x +。
解
()
()
()
()
222cos cos 2n n x
n x
n e e
x x π?
?=?=+ ??
?
则即得结果
A
6. 曲线
5
3y x x =+的凹区间是(B )
。
A.
(, 0) -∞; B. [0,]+∞; C. (, ) -∞+∞; D. 以上都不对。 解
2
1
3
355210
13
33y x y x -'''=+
=?=
当
()0, +x ∈∞时 , y <0'',>
7. 若
() (), () f x f x x -=-∞<+∞,在 (,="" 0)="" -∞内="" ()="">
f x '>且
() 0f x ''<,则在 (0,)="" +∞内有(="">
) 。
A.
() 0, () 0f x f x '''><; b.="" ()="" 0,="" ()="" 0f="" x="" f="" x="" '''="">>; C.
() 0, () 0f x f x '''<; d.="" ()="" 0,="" ()="" 0f="" x="" f="" x=""><>。
解 设
()0, x ∈+∞ 则 (), 0x -∈-∞
()()()()--f x f
x f x f x ''=∴-=
又
()()()-00f x f x f x '''>∴=--
由
()()-f x f x ''''= 且 ()0f x ''-<>
()0f x ''
8. 函 数
() y f x =
对 一 切
x 满
足
2
() 3[()]xf x x f x '''+1x e -=- ,
若
0() 0
f x '=,
0(0) x ≠则( B ) 。 A.
0() f x 是 () f x 的极大值; B. 0() f x 是 () f x 的极小值;
C.
0, 0(()) x f x 是曲线 () y f x =的拐点;
D.
0() f x 不是 () f x 的极值, 00(, ()) x f x 也不是曲线 () y f x =的拐点。
解
()0
00
011
x x x e e
f x x x e
---''=
=
当
()000
0x f x ''<>, 当 ()0000x f x ''>>
也即
()00f x ''≠,则 0x x =不是拐点
又
()00f x ''>, 则 0() f x 是 () f x 的极小值
三.解答题:
1. 求函数
2
ln () x f x x
=
的单调区间与极值。 (8分)
解 定义区间为
()
0, +∞,
令
()2
2
12ln ln x x x f x x
?
?-'=
2
2
2ln ln 0x x
x
-=
=
有
1x = 或者 2
x e
=
则在
2
(0,1]
[, ) e +∞单调减少 , 在 2
1, e ????上单调增加
极小值 :
()10f =, 极大值 :()2
2
4f e
e
=
2. 求下列极限。 (每小题 6分)
(1) 0
1
1
1
lim
() sin tan x x x
x
→-
解 原式 2
001
11cos 11lim () lim sin 2
x x x
x x x x x
→→-==?
=
(2) 1
ln cos(1) lim
1sin
2
x x x
π
→--
解 应用洛比塔法则 , 有
原式
()
()1
1
sin 1cos 1lim
cos
2
2
x x x x
π
π
→??--??-=-
()
()
2
2
1
1
tan 1sec
1lim
lim
cos
sin 2
2
22x x x x x
x
π
π
ππ→→--==??
- ???
2
4
π
-=
3. 确定函数
11
() 1x
x
f x e -=
-的间断点,并指出间断点所属的类型。 (8分)
解 函数在 x 0, x=1=处无定义 .
由于 010
l i m 110
x
x
x e e -→??-=-= ???
故
()0
lim x f
x →=
∞, 从而 0x =是 ()
f
x 的无穷间断点
又
1
1
lim ,
lim 11x x x
x x
x
+
-
→→=-∞=+∞--, 故
111
1
lim 0,
lim x x x
x
x x e
e e
e +--∞
+∞
--→→====+∞
所以
()()1
0,
1
1
f f -
+
==, 因此
1x =是 ()
f
x 的跳跃间断点
4. (8 分 ) 设 函 数
()
f x 在
[0,1]
上 连 续 , 在
(0,1)
内 可 导 , 且
1
(0)(1)0, () 12
f f f ===,证明:
(1) 存在 1
(,1) 2
η∈,使 () f ηη=;
(2) 存在 (0,1)ξ∈,使得 () () 1f f ξξξ'-+=。
证
(1) 设 ()()F x f x x =-
由
() f x 在 [0,1]上连续,在 (0,1)内可导
则 ()F x 在
1,12??????
上连续 , 可导 在
1,12??????上 111
111022222F f ????=-=-=> ? ?????
()()1110110F f =-=-=-
由零点定理 , 在
1, 12??
?
??
内至少存在一点
η, 使 ()0F η=
即
()
f
ηη
=
(2)设 ()
()x
f
x x
G
x e
-
=
, ()G
x 在 []0, η上连续 , 在
()0, η内可导 , 且 ()
()
00
00
f
G e
-=
=
()()0f G e ηηηη
-== 则在 ()
0, η内至少存在一点 ξ, 使 ()()()210f e f e G e ξξξξξξξ
'????---????'== 即 ()()10f e f e ξξξξξ'?
???---=???? 则
() () 1f f ξξξ'-+= 因为 ()
()0, 0, 1η?, 则 ()0, 1ξ∈, 即结论成立
范文三：大学英语期末考试题..
大学英语2、3级期末考试题型
题型如下：
Part I Listening Comprehension 20% (20 minutes) Part II Reading Comprehension 30% (35 minutes) Part III Vocabulary and Structure 15% (20 minutes)
[注意 本部分有2种题型]
Part IV Cloze 10% (10 minutes) Part IV Reading in Depth 10% (10 minutes) Part V Sentence Translation 10% ( 5 minutes) Part VI Writing 15% (30 minutes) ___________________________________________________ 100% 120 min.
Part I Listening Comprehension 20% (20 minutes) Section A Short Conversations
Directions: In this section, you will hear 3 conversations. At the end of each conversation, some
questions will be asked about what was said. Both the conversation and the questions will be spoken only once. After each question there will be a pause. During the pause, read the four choices marked A, B, C and D, and decide which is the best answer.
试题 1 – 10
（试题从课外出，难度等同于相应各级难度。）
Section B Short Passages
Directions: In this section, you will hear 3 short passages. At the end of each Passage, you will
hear some questions. Both the passage and the questions will be spoken only once. After you hear a question, choose the best answer from the four choices marked A, B,
C and D.
试题 11 – 20
（试题从课外出，难度等同于相应各级难度。）
（注：Section B会有复合式听写）
Part II Reading Comprehension (35 minutes)
Section A Skimming and Scanning 10% (15 minutes)
Directions: In this part, you will have 15 minutes to go over one long passage quickly and answer
10 questions about the passage. Choose the best answer from the four choices marked
A), B), C) and D). You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the center.
（试题从课外出，难度应等同于相应各级难度。）
Section B Passage Reading Skill 20% (20 minutes)
Directions: There are 2 passages in this part. Each passage is followed by some questions or
unfinished statements. For each of them there are four choices marked A), B), C) and
D). You should decide on the best choice and mark the corresponding letter on the
Answer Sheet with a single line through the center.
Passage One
Questions 31 to 35 are based on the following passage.
试题 31 – 35
（试题从课外出，难度等同于相应各级难度。）
Passage Two
Questions 36 to 40 are based on the following passage.
试题 36 – 40
（试题从课外出，难度等同于相应各级难度。）
Part III Vocabulary and Structure 15% (20 minutes)
Directions: There are 30 incomplete sentences in this part. For each sentence there are four
choices marked A), B), C) and D). Choose the ONE answer that best completes the
sentence. Then mark the corresponding letter on the Answer Sheet with a single line
through the center.
试题 41 – 70
（试题从每册教材中出，其指导思想是让学生重视教材。）
【注意：本大题有2种题型】
Part IV Cloze 10% (10 minutes)
Directions: There are 20 blanks in the following two passages. For each blank there are four
choices marked A), B), C) and D) on the right side of the paper. You should choose
the ONE that best fits into the passage. Then mark the corresponding letter on the
Answer Sheet with a single line through the center.
本部分试题有变化，试题 71 – 90
试题从教材的背诵段落出题，注意应该有一定的长度，1、2册出7套，3、4册出
6套。
样 题
When it comes to eating smart for your heart, thinking about short-term fixes and simplify life with a straightforward approach that will serve you well for years to come.
Smart eating goes beyond analyzing every bite ad you lift __71__ your mouth.
Scientists now __77__ on the broader picture of the balance of food eaten __78__ several days or a week __79__ than on the number of milligrams (毫克) of this or that __80__ at each meal.
Fruits, vegetables and whole grains, for example, provide nutrients and plant-based compounds __81__ for good health. “The more we learn, the more __82__ we are by the wealth
of essential substances they __83__,
You'll automatically be __85__ the right heart-healthy track if vegetables, fruits and whole grains make __86__ three quarters of the food on your dinner plate. __87__ in the remaining one quarter with lean meat or chicken, fish or eggs.
The foods you choose to eat as well as those you choose to __88__ clearly contribute to your well-being. Without a __89__, each of the small decisions you make in this realm can make a big __90__ on your health in the years to come.
71. A) between B) through C) inside D) to
72. A) serious B) splendid C) specific D) separate
73. A) key B) point C) lead D) center
74. A) strict B) different C) typical D) natural
75. A) rescue B) prevent C) forbid D) offend
76. A) in B) upon C) for D) by
77. A) turn B) put C) focus D) carry
78. A) over B) along C) with D) beyond
79. A) other B) better C) rather D) sooner
80. A) conveyed B) consumed C) entered D) exhausted
81 A) vital B) initial C) valid D) radical
82. A) disturbed B) depressed C) amazed D) amused
83. A) retain B) contain C) attain D) maintain
84. A) interfere B) interact C) reckon D) rest
85. A) at B) of C) on D) within
86. A) out B) into C) off D) up
87. A) Engage B) Fill C) Insert D) Pack
88. A) delete B) hinder C) avoid D) spoil
89. A) notion B) hesitation C) reason D) doubt
90. A) outcome B) function C) impact D) commitment
Part IV Reading in Depth 10% (10 minutes)
Direction: In this section, there is a passage with ten blanks. You are required to select one word
for each blank from a list of choices given in a word bank following the passage. Read the passage through carefully before making your choices. Each choice in bank is identified by a letter. Please mark the corresponding letter for each item on Answer Sheet 2 with a single line through the center. You may not use any of the words in the bank more than once.
本部分试题有变化，试题 71 – 80
本题型是从15个词中选10个词。试题从教材中Text A非背诵段落出题，注意应
该有一定的长度，1、2册出3套，3、4册出4套。
样 题
Questions 71 to 80 are based on the following passage.
In families with two working parents, fathers may have more impact on a child's language development than mothers, a new study suggests.
Researchers __71__ 92 families form 11 child care centers before their children were a year old, interviewing each to establish income, level of education and child care arrangements. Overall, it was a group of well-class families, with married parents both living in the home.
When the children were 2, researchers videotaped them at home in free-play sessions with both parents, __72__ all of their speech. The study will appear in the November issue of The Journal of Applied Developmental Psychology.
The scientists measured the __73__ number of utterance (话语) of the parents, the number of different words they used, the complexity of their sentences and other __74__ of their speech. On
average, fathers spoke less than mothers did, but they did not differ in the length of utterances or proportion of questions asked.
Finally, the researchers __75__ the children's speech at age 3, using a standardized language test. The only predictors of high scores on the test were the mother's level of education, the __76__ of child care and the number of different words the father used.
The researchers are __77__ why the father's speech, and not the mother's, had an effect.
A) already B) analyzed C) aspects D) characters
E) contributing F)describing G) established H) quality
I) quoted J) recording K) recruited L) total
M) unconscious N) unsure O) yet
Part IV Sentence Translation 10% ( 5 minutes) Directions: Read the following sentences carefully and then translate them into English. Your
translation must be written neatly on Answer Sheet.
整句翻译，不是半句翻译。
每套题都有，都是5句整句翻译，属于必出题。
共5句，把整句中文翻译成英文。
Part VI Writing 15% (30 minutes)
Directions: For this part, you are allowed 30 minutes to write a short essay on the topic of
Buying Commodities on Line. You should write at least 120 words following the
outline given bellow:
Buying Commodities Online
1. 网上购物成为时尚；
2. 与传统购物相比，网上购物的优势；
3. 你的看法。
范文四：大学英语期末考试题
1. Clara was ______to sell her late husband's paintings to pay her debts.
A) qualified for
B) assumed AN ASUMMED INCREASE IN POPULATION
C) compelled
D) racked to rack my brain
2. The new machine ______ seeds evenly and quickly over the whole field.
A) switched SWITCH ON/OFF
B) controlled MONITORED
C) risked
D) distributed
3. Breaking Mary’s doll was purely _____; John did not mean to do it.
A) occasional
B) accidental
C) casual
D) incidental
4. I was ___ the point of telephoning him when his letter arrived.
A) to
B) on
C) at
D) in
5.The professor______the whole chapter, saying it was not difficult for us to study it by ourselves.
A) dismissed
B) covered
C) skipped
D) explored
6. When her mother came back, she _____ in the sofa watching TV.
A) curled up
B) called up
C) setting up
D) torn up
7.The government has ______ defense spending.
A) cut away
B) cut across
C) cut back on
D) cut through
8.It seemed for a while that infants were ______ to AIDS.
A) contribute
B) attend
C) attribute
D) immune
9.Dr. Smith is starting the first training program himself, and his methods of teaching will be used
in all _____training programs.
A) subsequent
B) temporary
C) fruitful
D) energetic
10.This is a very formal occasion. It is not appropriate to wear_______pants or skirts.
A) Messy
B) frantic
C) casual
D) jealous
11.The noise________to be just the dogs fighting for a bone in the courtyard.
A) made out
B) worked out
C) rang out
D) turned out
12.Our system has been designed to give the user quick and easy__________to the required
information.
A) accent
B) access
C) response
D) approach
13.If school children are allowed to work at their own__________, their performance will
generally improve.
A) version
B) pace
C) evolution
D) system
14.Why did you have to __________the subject of religion since you know the guests are sharply
divided on it?
A) bring up
B) leave out
C) turn against
D) call up
15.The old lady took the cheese and ______ to eat.
A) commended
B) commented
C) renounced
D) commenced
17.All the questions the police asked _________what she had been doing on the night of the
robbery.
A) brought up
B) revolved around
C) built on
D) singled out She has been singled out because of her best performance
18.Why did you have to __________the subject of religion since you know the guests are sharply
divided on it?
A) bring up
B) leave out
C) turn against
D) call up
19.The lawyer outlined the case to him, being careful not to ______anything important.
A) save up
B) leave out
C) take out
D) cut through
20.The mother didn’t know who ______ for the broken glass.
A) blamed
B) be blamed
C) to blame
D) would blame
21.The manager finally changed his mind under ____.
A) tension
B) obligation
C) press
D) pressure
发言人(spokesman) 明确表示总统在任何情况下都不会取消这次旅行。(circumstances) The spokesman made it clear that the president would not cancel the trip under any circumstances.
.杰克对书架上那些书一本也不了解，所以他的选择是很随意的。(arbitrary)
Jack did not know anything about any of the books on the bookshelf, so his choice was quite
arbitrary.
不打算努力工作的人就没有取得成功的可能。(intend/ chance)
People who do not intend to work hard will have no chance to get success.
许多大学生申请政府贷款交付学费。 (loan) Many American students apply for government loans to pay for their education/tuition.
Fill in the missing words
keys
1.Into
2. At
3. Before
4. Car
5. Station
6. Confirmed
7. Injured
8. Drunk
9 Jail
10.Charged
11. Court
12.Dismissed
13. But
14. Fine
15. Where
16. Killing
17.From
18. Up
19. Fine
20. Free
范文五：概率论与数理统计C(中国农业大学)期末考试题
中国农业大学
2005~2006学年第 一 学期 (2005.12)
概率论与数理统计 (B)试题 (A卷 ) 课程考试试题
一 . 选择题(14分 , 每题 2分)
1. 如果 成立,则事件 A 与 B 互为对立 .
(A)Φ=AB ; (B) S B A = ; (c) Φ=AB 且 S B A = ; (D) A 与 B 互不相容 .
2.某人射击中靶的概率为 0.75. 若射击直到中靶为止,则射击次数为 3 的概率为 .
(A ) 3) 75. 0(; (B ) 2) 25. 0(75. 0; (C ) 2) 75. 0(25. 0; (D ) 3
) 25. 0(. 3.设 ) , (Y X 的联合概率密度为:???<+=,>
0; 1, /1) , (22他 其 y x y x f π
则 X 与 Y 为 的随机变量 . (A ) 独立同分布; (B ) 独立不同分布; (C ) 不独立同分布; (D ) 不独立不同分布 . 4. 总体未知参数 θ的估计量 θ?是 .
(A ) 随机变量 ; (B ) 总体 ; (C ) θ ; (D ) 均值 .
5. 设 Y X , 均服从正态分布,则协方差 0) , (=Y X Cov 是 Y X 与 相互独立的 ______________.
(A ) 充分条件 ; (B) 必要条件 ; (C ) 充要条件 ; (D) 既不充分又不必要条件 .
6.设 n X X X , , , 21 是来自总体 X 的简单随机样本,则 __________________.
(A ) n X X X , , , 21 同分布 ; (B ) n X X X , , , 21 与 X 同分布 ;
(C ) n X X X , , , 21 独立同分布 ; (D ) n X X X , , , 21 与 X 相互独立 .
7. 总体 X~N(a , σ2) ,期望 a 未知,要检验假设 0H :σ=σ0 (σ0为已知常数 ) ,使用统计量 ______________.
(A ) n a
X /σ-; (B ) n s a X /-; (C ) 22ns σ; (D ) 22) 1(σs n -.
二、填空题(16分 每空 2分)
1. 设 3/2) (3) (==B P A P , A 与 B 都 不 发 生 的 概 率 是 A 与 B 同 时 发 生 的 概 率 的 2倍 , 则 =-) (B A P
2. 设 X ~) 49, (a N ,则 ) (X E = ) (X D ) (2
X E = 3. 设 51, , X X 为 来 自 于 总 体 ) 1, 0(N 的 样 本 , 则 ~521X X X +++ ;
252221X X X +++ ~ .
考生诚信承诺
1. 本人清楚学校关于考试管理、考场规则、考试作弊处理的规定,并严格遵照执行。
2. 本人承诺在考试过程中没有作弊行为,所做试卷的内容真实可信。
专业: 班级: 学号: 姓名: 成绩:
4. 从总体 ξ中抽取简单随机样本 n X X , , 1 , X 是样本均值, 2
S 是样本方差, a E =) (ξ, 2) (σξ=D , 则 =) (X E ____________, =) (2S E _____________.
三、计算题 (70分 )
1. (10分 ) 编号为 1, 2, 3的三台仪器正在工作的概率分别为 0.9,0.8和 0.4, 从中任选一台.
(1) 求此台仪器正在工作的概率;
(2) 已知选到的仪器正在工作,求它编号为 2的概率.
2. (9分 ) 设随机变量 X 的密度函数为 :1() 0.4
133
k x F x x r x <><>
; 求 : (1) k; (2) r; (3).) 20(≤
3. (18分 ) 设二维随机变量 ( X , Y ) 的联合密度函数为:
???≤≤≤≤=. , 0, 10, 10, ) , (他 其 y x cxy y x f
试求 (1) 系数 c ; (2) ) (Y X P <; (3)="" )="" x="" f="" y="" x="" ;="" (4)="" x="" 与="" y="">
4.(9分 ) 设总体 ) 100, 72(~N X , n X X , , 1 为简单随机样本 , 为使样本均值大于 70
的概率不小于 90%,则样本容量至少取多少 (Φ(1.29)≈0.9)?
5. (12分 ) 设总体 X 的分布函数为 /, x 21xe x>0f(x)=0, x0
θθ-????≤?
其中 0θ>是未知参数, n X X , , 1 为来自总体 X 的简单随机样本,
求:(1)θ的矩估计量; (2) θ的极大似然估计量 .
6. (12分 ) 某冶金实验室对锰的熔化点作了四次试验,结果分别为
12690C 12710C 12630C 12650C
设数据服从正态分布 ) , (2
σμN ,
(1) 检验可否认为锰的熔化点的期望为 12600C ? (2) 求测定值的方差置信水平为 α-1的置信区间
(α=0.05) . 注: 1318. 2) 4( , 7764. 2) 4( , 3534. 2) 3( , 1824. 3) 3(05. 0025. 005. 0025. 0====t t t t ,
, 348. 9) 3(2025. 0=χ , 815. 7) 3(205. 0=χ , 143. 11) 4(2025. 0=χ , 488. 9) 4(2
05. 0=χ , 216. 0) 3(2975. 0=χ , 352. 0) 3(2
95. 0=χ
, 484. 0) 4(2975. 0=χ
711. 0) 4(295. 0=χ.
