-
试卷装订
线
2018
-2019
学年第一学期期末考试
B
卷
开课单位:
应用数学学院
课程名称:
Probability and
Statistics
任课教师:
考试类型:
闭卷
考试时间:
120
分钟
学院
姓名
学号
班级
题号
得分
阅卷人
一
二
三
总分
(本试卷共
4
页,满分
100
分)
---------------------------------
--------------------------------------------------
-------------------
I.
Fill in the blanks (3 points for each
blank, 18 points in total)
e
three events A
,
B
,
C , then the event that A, B and C not
happen can be denoted
as
2.
Suppose
P
(
A
p>
B
)
?
0.7
p>
,
P
(
A
)
?
0.3
A
a
nd B there is
no
intersection
,
then
P
(
B
)
p>
?
3.
Suppose
X
and
Y
are random events,
< br>D
(
X
)
?
4
D
(
Y
)
?
1
?
p>
XY
?
0
.
6
,then
D
(
3
X
?
2
p>
Y
)
?
_____
_
1
1
1<
/p>
4.
The probability
that three people can decipher a code
independently is
5
,
3
,
4
,
The probability of decoding the code.
=
5.
L
et's say that the random
variables X, Y
, and Z are independent
of each other
,
and
E
(
X
)
=5
E
(
Y
)
=11
,
E
(
Z
)
=8<
/p>
,
U=2X+3Y+1
;
V=YZ-4X.
then
E(V) =
,
E(U)
=
II. Choose the correct
answer (5 questions, 3 points each, 15 points in
total)
1.
Suppose
X~N
(
4
0
,
10
2
)
,
then
P( X < 45 )=
(
)
A
、
0.65
B
、
0.95
C
、
0.69
D
、
0.25
2.
Suppose that events A, B are
independent, and
P
(
A
)
?
p
,
P
(
B
p>
)
?
q
,
then
P
(
AB<
/p>
)
=
(
)
p>
A
、
p
(1
?
q
)
B
、
p
?
q
C
、
pq
p>
D
、
1
?
pq
3.
Suppose
X
~
?
(2)
,
Y
~
U
(1,3)
,
then
E
(2
X
?
3
Y
)
?
(
)
第
1
页
共
4
页
A
、
26
B
、
-2
C
、
-5
D
、
2
4.
Let's say
X
and
Y
are independent, and
E
(
X
)
=
< br>E
(
Y
)
=3
,
D
(
X
)
=12
,
D
(
Y
)
=1
6
,
Then
D
(
2
X
??
3
Y
)
=(
)
A
、
192
B
、
173
C
、
185
D
、
149
5
.
The following
are not criteria for evaluating
estimators.
(
)
A
.
consistency
B.
unbiasedness
C
.
effectiveness
D.
normality
III. Calculation ( 7 questions,
67 points in total)
1
、
(
7
points
)
The
probability of snow falling somewhere is
0.3
,
The probability of rain
is
0.5
,
The
probability of both snow
and rain is 0.1, calculate
:(
1
)
Probability of snow under
rain conditions
;
(
2
)
Probability of rain or snow on that day
.
.
2
、(
12
points
)
Let A
building material company have A, B, C 3 factories
produce the same
product, the output
takes up 50% of the whole company in turn, 30%,
20% and the defective rate
of each
factory is 10%, 20%, 30%, now from A batch of
products any one, find (1) this is the
probability of defective.(2) if the
product obtained is known to be defective, the
probability that
the product is
produced by factory A this time.
3.
(
12
points
)
The distribution of a
random variable
X
is
:
X
0
1
第
2
页
共
4
页
2