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Сборник задач по высшей математике. Тестовые методы контроля знаний. В 3 томах. Т.3

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
σ
σ
σ
σ
)(X
M
x
xXM=)
(
=
i
1
=
i
1
(
,
x
D=σ
#   
y
,
xx
D=σ
).
yy
    
Y  X:
y
( )
xxryy
=
B
σ
, (5.43)
x
X  Y:
x
( )
yyrxx
=
B
σ
. (5.44)
y
 1. ,   #
X 3 5 7
n 80 15 5
    λ, ,     
λ−
x
λ
;0,
.0,0
xf
( )
=
xe
<
x
. )            (

 (# 
)   !   -
):
.
)#     (5.38)
k
1
=
x
n
x
,
ini

x –  #,
i
n – ix ,
i
k
=
nn
#7 #.
i
201

51580
+
+
λ
λ
966
,
0
=
γ
8=x
3=σ
100
=
n
σ+σ
x
σ
2
2
2
2
γ
2
γ
=
100
σ
n
σ+σ
1
=x .
( )
5,357155803
=++
    (29) § 16   -

=1)(XM , 
5,31=
, , ,
1
2
==λ
.
7
5,3
 2. *          -
 (), 
  
,  # 
,  #7 #
.
. .    -
,
     (5.40)
t
γγ
x
n
,
 

x ,
 
# ,
t
n
  ,
n – #7 #.
t
  '
γ
  5,  
=
γ
1
t
)(γ=
t
, 
γ
γ
.
2
966,0
 
 #   1 
483,0
==
, 
t
γ
)( =
t
γ
12,2
. 
=
2
z
x
1
=
)(
483,0
2
dzex
π
0
  -
t
γ
=
 
t
x
n
t
γγ
x
n
( ) ( )
 
312,2
202
=
636,0
636,8;364,7636,08;636,08, =+=
.
 3.  #  30     -
05,0
=
α
χ
χ
χ
χ<χ
χ>χ
χ
α
1−−=rSk
30=S
271230=−−=k
χ
05,0
=
α
27=k
=
χ
χ
χ<χ
=
χ
χ>χ
=
χ
   . % -
    

2
= {34, 38, 40, 43, 47} :
  -
) #',      ;
#) ',      # ­.
. "     #-
2
  
  
     ; 
 . $  

   #
2
. 2

2
  

2
2
2

,  S
2

, -
 # (), r –   # ­.
*   # k.
,
    (30)  
2
)(
mx
2
2
σ
exf
 2  (m σ),
)(
=
2
πσ
, 
1
.
 #    
   

)  )  
  
2
,  34, 38, 40,   -
   #-
2

2
( 3),
1,40
.
    ,  
2
40
#'  ! 
.
)  #)   43 47  ,  
22
. *'  

2
43
.
22

. 8
 4.     #   #-     ( ):
203
x
y
µ
n
(
)
x
n
n
100
101020301020=+++++=
n
(
)
100
+++++
(
)
100
+⋅++⋅+⋅+⋅
⋅⋅+⋅⋅+⋅⋅+⋅⋅+⋅⋅+⋅⋅+⋅⋅+⋅⋅
1 2
0 20 0
1 0 10
3 30 20
5 10 10
. )#   
-
xy
  (5.41)
1
=µ yxxyn
xyxy
.
$ x, y (#' )  X Y,
n
  
xy
yx,
,
n#7 #,
,y – # .
* #    ' (5.38)
x
n ,yn –   x  y.

x
 
1
=
xn
,
x
1
=
y
yn
,
y
, 
1020102)103020(1 4,1
=x ,
=
10105)2030(3101200 6,2
=y .
=

=µ
xy
100
==
.16,064,38,36,24,1
 5. * #    : ) Y  X, #) X  Y,
204
102510152023301310210110202010
  # 
5,2=x
2,5=y
=
=
=
B
σ
2,22,
1
+
=
x
y
σ
27,053,
0
=
y
x
,
, #


r .
D , 36,0
x
8,0
16,0
D , # !  -
y
. ) " #   
 Y  X (5.43)
y
( )
xxryy
= .
B
σ
x
 
D=σ
,
xx
D=σ
yy

4,016,0
x
==σ
,
y
6,036,0 ==σ
.
)   
6,0
( )
8,02,5 =
xy
5,2
, 
.
4,0
#) " #     X
 Y (5.44)
x
( )
=
B
σ
y
yyrxx
.
    
4,0
8,05,2 =
( )
yx
2,5
, 
.
6,0
)  989 – 997     #     λ, ,   ­    
λ−
x
λ
<
;0,
.0,0
=
)(
xf
 
xe
x
989.
x
n
i
i
1 2 3
50 30 20
: 0,71
205
990.
γ
σ
95,0
=
γ
=
x
,
=
σ
,
=
n
,
)96,3;04,0(
95,0
=
γ
=
x
,
=
σ
,
=
n
,
)98,3;02,2(
x
i
0 2 4
991.
992.
993.
994.
995.
n
i
x
i
n
i
x
i
n
i
x
i
n
i
x
i
n
i
x
i
50 30 20
2 4 6
50 30 20
1 3 5
60 30 10
1 4 7
60 30 10
1 5 9
60 30 10
1 2 3
: 0,59
: 0,29
: 0,5
: 0,4
: 0,33
996.
997.
n
i
x
i
n
i
x
i
n
i
70 20 10
1 3 5
70 20 10
1 4 7
70 20 10
: 0,71
: 0,56
: 0,46
)  998 – 1006             ,  :  -
 ()
 
, # x,  
 #7 # n.
998.
999.
2
3
10
5
100. :
100. :
206
1000.
95,0
=
γ
=
x
,
=
σ
,
=
n
,
)49,4;51,3(
1001.
97,0
=
γ
=
x
,
=
σ
,
=
n
,
)36,1;64,0(
1002.
97,0
=
γ
=
x
,
=
σ
,
=
n
,
)72,2;28,1(
1003.
97,0
=
γ
=
x
,
=
σ
,
=
n
,
)
085
,6;
915
,3(
1004.
989
,
0
=
γ
=
x
,
=
σ
,
=
n
,
)27,7;73,4(
1005.
989
,
0
=
γ
=
x
,
=
σ
,
=
n
,
)08,21;92,1
(
1006.
989
,
0
=
γ
=
x
,
=
σ
,
=
n
,
)27,1;27,1(
χ
α
1007.
01,0
=
α
=
n
,
=
χ
1008.
01,0
=
α
=
n
,
=
χ
1009.
01,0
=
α
=
n
,
=
χ
1010.
025
,
0
=
α
=
n
,
=
χ
1011.
025
,
0
=
α
=
n
,
=
χ
1012.
025
,
0
=
α
=
n
,
=
χ
1013.
05,0
=
α
=
n
,
=
χ
1014.
05,0
=
α
=
n
,
=
χ
1015.
05,0
=
α
=
n
,
=
χ
χ
α
4
5
400. :
1
2
5
6
7
0
5
10
15
5
20
10
900. :
900. :
900. :
100. :
100. :
400. :
)  1007 – 1015  #'   
2
 ,      
       
,  #  n .
12
14
24
2
,
,
,
,
,
,
(18; 20; 22; 24; 26).
2
(19; 25; 31; 36; 40).
2
(30; 32; 34; 36; 38).
2
,
,
,
(16; 18; 20; 22; 24).
2
(16; 18; 20; 22; 24).
2
(28; 32; 36; 40; 44).
2
(14; 15; 17; 18; 20).
2
(12; 13; 15; 17; 19).
2
(18; 20; 22; 24; 26).
: 18
: 31
: 36
: 18
: 20
: 32
: 15
: 17
: 22
10
21
22
11
13
16
)  1016 – 1024  '   
2
 ,      
    #    
,  #  n .
207
1016.
01,0
=
α
=
n
,
=
χ
1017.
01,0
=
α
=
n
,
=
χ
1018.
01,0
=
α
=
n
,
=
χ
1019.
025
,
0
=
α
=
n
,
=
χ
1020.
025
,
0
=
α
=
n
,
=
χ
1021.
025
,
0
=
α
=
n
,
=
χ
1022.
05,0
=
α
=
n
,
=
χ
1023.
05,0
=
α
=
n
,
=
χ
1024.
05,0
=
α
=
n
,
=
χ
1025.
y
08,0
1026.
y
9,0
1027.
y
6,0
15
2
,
(15; 18; 22; 26; 30).
: 30
13
16
18
2
,
,
,
,
,
(28; 30; 32; 34; 36).
2
(27; 29; 31; 33; 35).
2
,
,
,
(18; 20; 22; 24; 26).
2
(22; 23; 24; 25; 26).
2
(20; 25; 29; 32; 37).
2
(25; 28; 30; 33; 38).
2
(26; 30; 34; 36; 39).
2
(28; 31; 32; 35; 36).
: 30
: 33
: 22
: 25
: 29
: 28
: 34
: 35
17
19
20
23
25
)  1025 – 1060  #   ­ ( )     # .
x
-2 -1 0 1
0 0 20 30 10
4 10 0 20 10
x
-2 -1 0 1
:
0 0 40 10 50
3 60 0 30 10
x
-2 -1 0 1
:
-3 10 10 0 20
3 10 20 30 0
208
:
1028.
x
y
63,0
1029.
y
02,0
1030.
y
1031.
y
1032.
y
4,0
1033.
y
1,0
-2 -1 0 1
-4 40 0 30 40
0 20 50 20 0
x
-1 0 1 2
-1 0 20 30 10
0 10 0 20 10
x
-1 0 1 2
1 10 10 0 20
2 10 0 20 30
x
-1 0 1 2
:
:
: 0,1
0 10 20 0 10
1 20 10 20 10
x
0 1 2 3
-1 10 0 10 30
1 10 10 30 0
x
0 1 2 3
-1 10 10 0 20
0 10 20 30 0
: 0,02
:
:
209
1034.
x
y
1035.
y
65,0
1036.
y
52,0
1037.
y
1038.
y
1039.
y
0 1 2 3
0 10 10 20 0
1 10 0 30 20
x
0 1 2 3
-2 30 0 40 60
2 20 10 40 0
x
1 2 3 4
0 0 10 10 20
2 30 0 20 10
x
1 2 3 4
: 0,18
:
:
0 0 40 10 10
1 10 0 10 20
x
1 2 3 4
-1 10 20 10 10
1 10 10 30 0
x
1 2 3 4
1 10 30 0 10
2 10 10 20 10
: 0,12
: 0
: 0,1
210
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